iMac tells me I have problem with iCloud password but it's correct

In updating my iMac it finished without completing and said enter Apple ID password. iMac responded with Can't connect because of problem with iCloud. to his enter Apple ID password. I get this 'endlessly.'

I know my iCloud/Apple ID password is correct because my iPhone works and so does my MacBook, and I can sign on Mac community.

How can I get out of this endless "Can't connect . . . Enter Apple ID password"?