You can only provide access to any Google products – such as Google Analytics – to a registered Google account.
When you access Google Analytics and attempt to add a user, it will ask you for the email address(es) of the user(s) who you want to add.
These email addresses have to be associated with a Google account.
A Gmail account will work, as Gmail accounts are Google accounts.
But you can also set-up a Google account for your gmu.edu email address.
This is the recommended method, as it keeps your personal Google account separate from your work account.
Here is a link you can use to create a Google account attached to your Mason email addresses: