Storage full error message

Hey MikaOK,
I can help you figure out why you are seeing the notification of not having enough storage space for your backup through iCloud.
The reason for this is that your iPhone back up may be bigger that 5 GB's that you have available to you. Go to Settings > iCloud > Storage > Manage Storage, you should see a list of backup's and probably just one that has the name of your iPhone with a heading underneath it that says This iPhone. Tap that and you will see what is taking up the most space. It could be things like Photos, Messages and other apps on your iPhone that are backed up through iCloud. Take a look at the article below for more details on managing your iCloud storage space.
Manage your iCloud storage
https://support.apple.com/en-us/HT204247

Select which iOS apps to back up

Many apps automatically back up to iCloud after you install them. You can change which apps back up to iCloud and remove existing backups of that app's data from your storage.

Use these steps on your iPhone, iPad, or iPod touch:

1. Tap Settings > iCloud.
   • If you're using iOS 8 or later, tap Storage > Manage Storage.
   • If you're using an earlier version of iOS, tap Storage & Backup > Manage Storage.
2. Tap the name of your iOS device.
3. Under Backup Options, turn off any apps that you don't want to back up. When you're asked to confirm, choose Turn Off & Delete to turn off Backup for that app and remove all of its data from iCloud.

Take care

I keep receive error message icloud storage is full when it's left more than 2GB space there. Can anyone help me with this error? If I sign out from icloud, it will delete files from my Mac.

Your backup is larger than 2GB. You need to reduce the size of your backup. You may want to delete other backups on iCloud. Signing out of iCloud will remove the iCloud files from your Mac, but they will be put back on the Mac when you sign back in.

Cheers,

GB

What is the size of your Notes file and your Pages file? What about Mail? Are you showing anything under "Other Documents"?

Go to Settings>General>Storage & iCloud Usage, then click on Manage Storage under iCloud and see what these items are using in storage.

Cheers,

GB

Try a reset.

Reset Device

But currently the problem is it keeps tell me icloud storage is full when I'm using Pages and Notes only.

Are you using automatic iCloud backups for your devices - i.e., do you back up your iOS devices to iCloud?

GB

I just check my iphone and icloud, it shows the backup is off. I still have 2GB+ storage size left but why it keeps telling me is full and won't save my notes and pages files to icloud.

Less than 100MB only. It shows more than 3GB free space but it keeps tell me storage is full. My mailbox used up 2GB++ but I no idea what causing the bug.