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Make an encrypted backup of your phone in iTunes on your computer and then go to Settings > General > Reset on your iPhone and choose for Erase All Content and Settings.
After that set your iPhone up as a new device and log on with your credentials in iCloud. Try enabling backup, iCloud Drive and photos and see what happens.
If it works, restore your iPhone from the backup you just made and see if iCloud still works for backup, iCloud Drive and Photos.
If the answer is no, then this means something was corrupted and you have to set up your iPhone as new in order to fully utilize iCloud.
If you have any further questions, please join our forum. We're happy to help.