Unlike the Plesk control pane which provides an option to change the password associated with usernames for mySQL, the CPanel control panel has no such option. That doesn't mean that you can't change the password though, it just means that you have to use a slightly less obvious way to do it. To change a password for a mySQL user via CPanel you perform the following steps:
SET PASSWORD FOR username = PASSWORD(password)
This method just makes use of the regular mySQL method of changing passwords that works completely independently of what control panel you are using.
You can also change the password when changing the permissions granted to the user via the GRANT mySQL command.
This article written by Stephen Chapman, Felgall Pty Ltd.