I had a problem with my calendar not syncing. I found that in Settings there is a section for Accounts and under Accounts there is a line for Google. I selected that line and the next screen had (at the top) Accounts and within it was my Gmail account. I selected that and got a long list of entries, one of which was Keep. You may have been there already but, if not, give that a try. My calendar is one of the entries and is now working fine.