First thing you need to know about deleting friends on your phone or tablet is that you can't delete Facebook friends directly on the game. If you want delete from 8 Ball Pool someone who is also your Facebook friend, you will have to remove them directly from your Facebook friends list and they should then disappear from the game.
People you add within the game itself, though, is different story! You can easily delete them by following these steps:
1. Open your app and tap on the Play With Friends option;
2. Once your friends list appears, tap on the Edit button as shown below;
3. The Challenge option will then change to Remove. If the Remove button appears greyed out, it means that person is your Facebook friend. Tap Remove on a user who is not Facebook friend and see what happens!
4. A wild confirmation screen appears! Make sure the nickname that shows on the screen belongs to the person you want to delete. Tap on Yes and that's it! That user was successfully removed.
*Each non-Facebook friend should have an X on the top right corner of your friends list item to remove.
Unfortunately you can't remove friends from Facebook. Maybe by removing specific friends from Facebook and then clear cache from both apps will work.