Problem because of two different iCloud accounts.

On my iPhone I have an iCloud account that uses an old @mac.com email. While on my iPad, my iCloud account uses my Gmail account. I would like my iPhone and iPad to use the same iCloud.com account and I want that account to use only my @gmail not my @mac email. Unfortunately, I can't seem to fix this problem.

I have tried the following:

1. I logged into iCloud.com with the @mac.com email and attempted to add the @gmail account. The response I get is, "This email account is already being used by another Apple ID." (Yes, that would be me.)
2. I logged into iCloud.com with the @gmail.com email and attempted to add the @mac.com email. The response I get is, "You cannot use this email address. Please try again using a different email address."

I would really like to delete the @mac.com account entirely and only use the Gmail account for iCloud. Your help would be very much appreciated.

Respectfully,

mrthayer