As suggested by @Hubert Dudek​ , please check your network settings, in case you have any firewall or rules that may be blocking the RDS connection on port 3306.

Also, check if you are whitelisting the correct endpoint as per your region.

To debug this further, you can SSH into one of the AWS worker instances used by a Databricks cluster and test the connectivity.

Eg: For us-east-1 region, run this command

nc -zv mdb7sywh50xhpr.chkweekm4xjq.us-east-1.rds.amazonaws.com 3306