A very easy one: just run a cronjob and it will back up databases from any server!
Change what's in red.
curl http://cPanelusername:firstname.lastname@example.org:2082/getsqlbackup/DB.gz --output /home/username/DB.gz
DB is the mysql database name which is something like username_dbname
Now FTP to your linux account and in the default home folder is the backup.