Nginx multiple server blocks listening to same port

Question

Create separately two files (you don't have to, but it will be much clearer) in /etc/nginx/sites-available/www.example.com and /etc/nginx/sites-available/api.example.com

The api.example.com file's conten

server {
        listen 80
        server_name api.example.com
        root /var/www/api.example.com/html/example/app; #also add a root dir here
        location / {
                proxy_set_header Host $host;
                proxy_set_header X-Real-IP $remote_addr;
                proxy_pass http://127.0.0.1:3836;
        }
}

The www.example.com's content:

server {
        listen 80 default_server;
#       listen [::]:80 default_server ipv6only=on;

        root /var/www/example.com/html/example/app;
        index index.html index.htm;

        # Make site accessible from http://localhost/
        server_name www.example.com www.example.org;

        location / {
                # First attempt to serve request as file, then
                # as directory, then fall back to displaying a 404.
                try_files $uri $uri/ =404;
                # Uncomment to enable naxsi on this location
                # include /etc/nginx/naxsi.rules
        }

        location /bower_components {
                alias /var/www/example.com/html/example/bower_components;
        }

        location /scripts {
                alias /var/www/example.com/html/example/scripts;
        }

        location /content {
                alias /var/www/example.com/html/example/content;
        }

        location /api {
                proxy_set_header Host $host;
                proxy_set_header X-Real-IP $remote_addr;
                proxy_pass http://127.0.0.1:3836;
        }
}

And finally enable the domains: sudo ln -s /etc/nginx/sites-available/www.example.com /etc/nginx/sites-enabled/www.example.com and sudo ln -s /etc/nginx/sites-available/api.example.com /etc/nginx/sites-enabled/api.example.com