A tricky little problem is when installing WHM on a new server, the option “Restrict outgoing SMTP to root, exim, and mailman (FKA SMTP Tweak)” is on by default. To allow your server to send emails using Gmail / Google Apps Email / or another external email provider you will need to turn this option off. Leaving this enabled causes the following error in WHMCS: SMTP Error: Could not authenticate.
Go to "Tweak Settings" in WHM
And search for “Restrict outgoing SMTP to root, exim, and mailman (FKA SMTP Tweak)”
See the screenshot below: