I recently changed my apple ID. Now I cant synchronise calendars and other things because my icloud email is still showing the old email (it is not functioning and I dont know the password). How to change the icloud email to same as Apple ID?

My Apple ID was linked to an old unused email address, so I recently changed it successfully to a new email address and password. However, none of my calendars will sync across devices (2 x phones, macbook air, ipad) now, and I get a pop up message saying icloud is not working because there is a problem with email address ..... (still shows the old one). When I go into system preferences to icloud, the old email ID is still showing, not the new one, it doesnt give me an option to change it. It just asks for the password connected to the (old) email - which I can't remember....

When I go into Apple ID support to look at my account, it shows my new (changed) email on my account, and also on the icloud info! (no where in the account is the 'old' email showing on icloud). I have two other addresses there, as secondary ones an @icloud.com and an @me.com - some forums have suggested adding the new email here but it wont accept it because what I try to change it to is my current Apple ID! There seems to be no way to get help from Apple about this, and I am becoming increasingly frustrated! All Apple things lead to me signing in and then giving options to change my Apple ID again! But I've already done that, I successfully changed my Apple ID, but unfortunately it is Apple that have not linked that to my icloud ID. What can I do, can anyone help? Very grateful to anyone who can suggest a way!