Recently we accidentally dropped a table from a MySQL database on our development server. The thought of extracting a 34 GB gzip file to get to the MySQL backup was a painful one.
Here is a simple way to export only the MySQL folder from a full cPanel backup. The MySQL folder contains a bunch of .sql files. Each .sql file is a dump of a single MySQL database from the account.
Run this command from the shell:
tar -xvf username.tar.gz mysql