export database

Try clicking the link inside the backups section of cPanel for the database you want to download. That should work fine with an average size DB. Or do a full system backup. That will backup all databases as well.

Those instructions IMO, leave out a step or two.

Open PHPAdmin click on name of DB on left.
On right side of page click Export.
In the Export box you see on right frame click select all.
to the right of that click Add Drop Table.
Down below that click Complete Inserts.
Down below that click save as file.
Give it a name, uncheck remember template, click your choice of compression and hit go.

Or back it up the best way via SSH.

mysqldump --opt -Q -u accountname_accountname -p accountname_databasename > /home/accountname/path/to/save/directory/databaseBU.12.05.06.works.sql

One of those should get you what you seek.