Adding a Google account for calendar purposes on iOS 8.3
Have you tried the following on your iOS device:
Add Account > Other > Add CalDAV Calendar
Then enter your credentials:
Server: google.com
Username: Enter the email address of the associated Google account.
Password: Enter the password that is associated with the Google account from above.
Description: Purely for information. Enter a description of the account.
This should work when only using the Calendar on a Google Account.