How can I change the iCloud account associated with my iphone

I changed my e-mail address a few months ago including changing my Apple ID to reflect my new e-mail. For some reason, my iphone and my ipad are both stuck with the iCloud username of my old e-mail address. When I try to delete these accounts like other forums have indicated to do, it won't let me because every password possible comes up as invalid and the "forgot password" e-mail never comes. I was wondering if there was a way to delete the icloud account associated with my old e-mail without having a password and replacing it with the updated iCloud information.