Cannot connect to Cloud SQL Postgres from GKE via Private IP

Solution 1:

There are specific network requirements Cloud SQL instances must adhere to when communicating via a private connection. One of which is that your CloudSQL and GKE instances are located in the same region and VPC network. [1]

Regarding "I cannot reach the database from within a container on the node", does this mean you have your database and container located in different networks? If so, you cannot access a Cloud SQL instance on its private IP address from another network using a Cloud VPN tunnel, instance based VPN, or Cloud interconnect.

[1] https://cloud.google.com/sql/docs/mysql/private-ip#network_requirements.