Q: Apple ID keeps asking for password for old email address

I have changed my email address on my Apple ID.  I have not set up a new Apple ID, it is under my old Apple ID, but my iPhone and iPad is constantly popping up with a request from iCloud to enter the password to my email address.  The password is still the same and despite entering the password, I am constantly asked to input the password for the old email address. Help!!! It's driving me nuts!!