I have installed a PostgreSQL on google cloud and I want to be able to access it remotely from my PC using preferably pg-admin.
I do get the following error when I try to connect to my instance:
Unable to connect to server:
could not connect to server: Connection refused (0x0000274D/10061) Is the server running on host "[external IP of my VM instance]" and accepting TCP/IP connections on port 5432?
I think this could because google cloud firewall is blocking me (maybe!), I specified the following firewall for my instance, I use my ip address to define  Source filters:

am I missing something because I cant still access this, can someone please help me I have no idea anymore, I have check many tutorials and I have done many things that I though should fix this. anyone any idea?
PostgreSQL must also be configured to allow remote connections, otherwise the connection request will fail, even if all firewalls rules are correct and PostgreSQL server is listening on the right port.
Couldn't create links, but this is a rather long answer so this may helps.
nc or netcatnmapnetstatlsof
postgresql.confpg_hba.conf
nc or netcat
$ nc -zv 4.3.2.1 5432
Where
 -v      Produce more verbose output.
 -z      Only scan for listening daemons, without sending any data to
         them.  Cannot be used together with -l.
Possible outcomes:
Connection to 4.3.2.1port [tcp/postgresql] succeeded!
Yay.
nc: connect to 4.3.2.1 port 8000 (tcp) failed: Connection refused
Port open by firewall, but service either not listening or refusing connection.
Firewall is blocking.
nmap
$ nmap 4.3.2.1
Starting Nmap 7.70 ( https://nmap.org ) at 2019-09-09 18:28 PDT
Nmap scan report for 1.2.3.4.bc.googleusercontent.com (4.3.2.1)
Host is up (0.12s latency).
Not shown: 993 filtered ports
PORT     STATE  SERVICE
22/tcp   open   ssh
80/tcp   closed http
443/tcp  closed https
3389/tcp closed ms-wbt-server
4000/tcp closed remoteanything
5432/tcp open   postgresql      # firewall open, service up and listening
8000/tcp closed http-alt        # firewall open, is service up or listening?
netstat
$ netstat -tuplen
(Not all processes could be identified, non-owned process info
 will not be shown, you would have to be root to see it all.)
Active Internet connections (only servers)
Proto Recv-Q Send-Q Local Address           Foreign Address         State       User       Inode      PID/Program name    
tcp        0      0 0.0.0.0:4000            0.0.0.0:*               LISTEN      1000       4223185    29432/beam.smp      
tcp        0      0 127.0.0.1:5432          0.0.0.0:*               LISTEN      1000       4020942    15020/postgres      
tcp        0      0 127.0.0.1:5433          0.0.0.0:*               LISTEN      1000       3246566    20553/postgres      
tcp6       0      0 ::1:5432                :::*                    LISTEN      1000       4020941    15020/postgres      
tcp6       0      0 ::1:5433                :::*                    LISTEN      1000       3246565    20553/postgres      
udp        0      0 224.0.0.251:5353        0.0.0.0:*                           1000       4624644    6311/chrome --type= 
udp        0      0 224.0.0.251:5353        0.0.0.0:*                           1000       4624643    6311/chrome --type= 
udp        0      0 224.0.0.251:5353        0.0.0.0:*                           1000       4625649    6230/chrome         
udp        0      0 0.0.0.0:68              0.0.0.0:*                           0          20911      -                   
udp6       0      0 :::546                  :::*                                0          4621237    -                   
where
-t | --tcp
-u | --udp
-p, --program
    Show the PID and name of the program to which each socket belongs.
-l, --listening
    Show only listening sockets.  (These are omitted by default.)
-e, --extend
    Display additional information.  Use  this  option  twice  for  maximum
    detail.
--numeric, -n
    Show numerical addresses instead of trying to determine symbolic  host,
    port or user names.
When issued on the instance where PostgreSQL is running, and you don't see the lines below, it means that PostgreSQL is not configured for remote connections:
tcp        0      0 0.0.0.0:5432            0.0.0.0:*               LISTEN      1001       238400     30826/postgres
tcp6       0      0 :::5432                 :::*                    LISTEN      1001       238401     30826/postgres  
lsof
To check on instance whether service is running at all.
$ sudo lsof -i -P -n | grep LISTEN
 systemd-r   457 systemd-resolve   13u  IPv4  14870      0t0  TCP 127.0.0.53:53 (LISTEN)
 sshd        733            root    3u  IPv4  19233      0t0  TCP *:22 (LISTEN)
 sshd        733            root    4u  IPv6  19244      0t0  TCP *:22 (LISTEN)
 postgres   2733        postgres    3u  IPv4  23655      0t0  TCP 127.0.0.1:5432 (LISTEN)
 python3   26083        a_user      4u  IPv4 392307      0t0  TCP *:8000 (LISTEN)
To connect from your end, you will need the public IP address of your box, and that of the Google Compute Engine (GCE) instance.
(From this article.)
$ dig +short myip.opendns.com @resolver1.opendns.com
4.3.2.1
$ gcloud compute instances list
NAME         ZONE        MACHINE_TYPE   PREEMPTIBLE  INTERNAL_IP  EXTERNAL_IP     STATUS
access-news  us-east1-d  n1-standard-2               10.142.0.5   34.73.156.19    RUNNING
lynx-dev     us-east1-d  n1-standard-1               10.142.0.2   35.231.66.229   RUNNING
tr2          us-east1-d  n1-standard-1               10.142.0.3   35.196.195.199  RUNNING
If you also need the network-tags of the instances:
$ gcloud compute instances list  --format='table(name,status,tags.list())'
NAME         STATUS   TAGS
access-news  RUNNING  fingerprint=mdTPd8rXoQM=,items=[u'access-news', u'http-server', u'https-server']
lynx-dev     RUNNING  fingerprint=CpSmrCTD0LE=,items=[u'http-server', u'https-server', u'lynx-dev']
tr2          RUNNING  fingerprint=84JxACwWD7U=,items=[u'http-server', u'https-server', u'tr2']
Dealing only with GCE firewall rules below, but make sure that iptables doesn't inadvertently blocks traffic.
See also
iptables$ gcloud compute firewall-rules list
NAME                      NETWORK  DIRECTION  PRIORITY  ALLOW                         DENY  DISABLED
default-allow-http        default  INGRESS    1000      tcp:80                              False
default-allow-https       default  INGRESS    1000      tcp:443                             False
default-allow-icmp        default  INGRESS    65534     icmp                                False
default-allow-internal    default  INGRESS    65534     tcp:0-65535,udp:0-65535,icmp        False
default-allow-rdp         default  INGRESS    65534     tcp:3389                            False
default-allow-ssh         default  INGRESS    65534     tcp:22                              False
pg-from-tag1-to-tag2      default  INGRESS    1000      tcp:5432                            False
To show all fields of the firewall, please show in JSON format: --format=json
To show all fields in table format, please see the examples in --help.
A more comprehensive list that includes network-tags as well (from gcloud compute firewall-rules list --help):
$ gcloud compute firewall-rules list --format="table(     \
      name,                                               \
      network,                                            \
      direction,                                          \
      priority,                                           \
      sourceRanges.list():label=SRC_RANGES,               \
      destinationRanges.list():label=DEST_RANGES,         \
      allowed[].map().firewall_rule().list():label=ALLOW, \
      denied[].map().firewall_rule().list():label=DENY,   \
      sourceTags.list():label=SRC_TAGS,                   \
      sourceServiceAccounts.list():label=SRC_SVC_ACCT,    \
      targetTags.list():label=TARGET_TAGS,                \
      targetServiceAccounts.list():label=TARGET_SVC_ACCT, \
      disabled                                            \
  )"
NAME                      NETWORK  DIRECTION  PRIORITY  SRC_RANGES    DEST_RANGES  ALLOW                         DENY  SRC_TAGS  SRC_SVC_ACCT  TARGET_TAGS   TARGET_SVC_ACCT  DISABLED
default-allow-http        default  INGRESS    1000      0.0.0.0/0                  tcp:80                                                      http-server                    False
default-allow-https       default  INGRESS    1000      0.0.0.0/0                  tcp:443                                                     https-server                   False
default-allow-icmp        default  INGRESS    65534     0.0.0.0/0                  icmp                                                                                       False
default-allow-internal    default  INGRESS    65534     10.128.0.0/9               tcp:0-65535,udp:0-65535,icmp                                                               False
default-allow-rdp         default  INGRESS    65534     0.0.0.0/0                  tcp:3389                                                                                   False
default-allow-ssh         default  INGRESS    65534     0.0.0.0/0                  tcp:22                                                                                     False
pg-from-tag1-to-tag2      default  INGRESS    1000      4.3.2.1                    tcp:5432                            tag1                    tag2                           False
To open the default PostgreSQL port (5432) from every source to every instance:
$ gcloud compute firewall-rules create \
    postgres-all                       \
    --network default                  \
    --priority 1000                    \
    --direction ingress                \
    --action allow                     \
    --rules tcp:5432                   \
To restrict it between your computer (source: YOUR_IP) and the GCE instance (destination: INSTANCE_IP):
$ gcloud compute firewall-rules create \
    postgres-from-you-to-instance      \
    --network default                  \
    --priority 1000                    \
    --direction ingress                \
    --action allow                     \
    --rules tcp:5432                   \
    --destination-ranges INSTANCES_IP  \
    --source-ranges YOUR_IP            \
Instead of --source-ranges and --destination-ranges one could use source and target network tags or service accounts as well. See the "Source or destination" section in the firewall docs.
This is an update to Neeraj Singh's post.
By default PostgreSQL is configured to be bound to “localhost”, therefore the configuration files below will need to be updated:
postgresql.conf, and
pg_hba.conf
The location of both files can be queried from PostgreSQL itself (trick taken from this Stackoverflow thread):
$ sudo -u postgres psql -c "SHOW hba_file" -c "SHOW config_file"
postgresql.conf
The configuration file comes with helpful hints to get this working:
listen_addresses = 'localhost'          # what IP address(es) to listen on;
                                        # comma-separated list of addresses;
                                        # defaults to 'localhost'; use '*' for all
                                        # (change requires restart)
For a quick and dirty solution just change it to
listen_addresses = '*'
Restart the server (see here how). Once PostgreSQL is restarted, it will start listening on all IP addresses (see netstat -tuplen).
To restart PostgreSQL:
$ sudo systemctl restart postgresql@11-main
# or
$ pg_ctl restart
The listen_addresses documentation says that it "Specifies the TCP/IP address(es) on which the server is to listen for connections from client applications.", but that's all. It specifies the sockets the packets are accepted from, but if the incoming connections are not authenticated (configured via pg_hba.conf), then the packets will be rejected (dropped?) regardless.
pg_hba.conf
From 20.1. The pg_hba.conf File: "Client authentication is controlled by a configuration file, which traditionally is named pg_hba.conf and is stored in the database cluster's data directory. (HBA stands for host-based authentication.)"
This is a complex topic so reading the documentation is crucial, but this will suffice for development on trusted networks:
host    all   all   0.0.0.0/0   trust
host    all   all   ::/0        trust
Another restart is required at this point.
I followed the tutorial on 1 and I could connect remotely from one machine to another. I could reproduce your case by miss configuring the firewall rules. You have set the firewall rule with a tag. That tag needs to be on the VM too. If you create a firewall rule with a tag, that tag needs to be on(in my case the tag name for the tag is postgre-5432) Network Tags:

You can Edit your Compute Engine instance on the VM instance section.
In this case tags are used to be able to set firewall rules in the same network for a specific machine.
Here is the definition of my firewall rule for ingress traffic. This is the tag that my Compute Engine Instance running postgresql server has configured on the Network Tags section:

In source Ip ranges you need to place the PUBLIC IP address of the computer that you want to connect from, to the computer running the postgresql server as this is an ingress firewall rule. And with that ip as source ip you shouldn’t have any tag problem. I encourage you to use tags as everything will be more secure.
You can check the PUBLIC IP of your local connection in this address: http://ip4.me/
Then on the configuration files you mentioned you need to place the Public IP of your connection . This IP needs to be the same that you are using on your ingress firewall rule.
sudo nano /etc/postgresql/9.5/main/pg_hba.conf: host all all PUBLIC_IP/32 md5
And here you need to set * for the listen_addresses as * means any address. Anyway you are controlling the ips able to connect to your instance in pg_hba.conf:
sudo nano /etc/postgresql/9.5/main/postgresql.conf listen_addresses = '*' # what IP address(es) to listen on;
pgAdmin:
Here you can see how to install pgAdmin4 on ubuntu 2 Here you can see how to connect to postgres from the command line. [3
To be able to connect to your postgres remote instance from pgAdmin4 you need to set the host-name/address to your Compute Engine Instance Ip running your postgresql server. If you followed the tutorial here 1 you should have a default database named postgres too.

Hope this helps!
1 https://cloud.google.com/community/tutorials/setting-up-postgres#creating-a-compute-engine-instance
2 https://askubuntu.com/questions/831262/how-to-install-pgadmin-4-in-desktop-mode-on-ubuntu
3 https://www.postgresql.org/message-id/001f01c018c2$830133b0$64898cd5%40northlink.gr
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