This bits working great:
 SELECT products_id, sum(attributes_stock) 
 FROM products_attributes 
 GROUP BY products_id
Which adds together all the groups of fields in the attributes_stock column.
What I am having trouble with is getting this result to UPDATE another column in another table.
This is what I have:
 UPDATE products, products_attributes 
 SET products.products_quantity = sum(products_attributes.attributes_stock) GROUP BY products_attributes.products_id 
 WHERE products.products_id = products_attributes.products_id
Any advice greatly appreciated.
You can't use a group by inside an update statement.  You'll need to use an sub select to do the grouping.
Something like this:
UPDATE products p,( SELECT products_id, sum(attributes_stock)  as mysum
                   FROM products_attributes GROUP BY products_id) as s
   SET p.products_quantity = s.mysum
  WHERE p.products_id = s.products_id
                        Some favor the newer-style JOIN ... ONsyntax for a join operation, vs. the comma operator and the join predicate in the WHERE clause:
UPDATE products p
  JOIN ( SELECT q.products_id
              , SUM(q.attributes_stock) AS sum_attr
           FROM products_attributes q
          GROUP BY q.products_id
       ) r
    ON r.products_id = p.products_id
   SET p.products_quantity = r.sum_attr
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