I understand that the Prince of Wales was caned a few times at Gordonstoun School in Scotland for “ragging” which is fighting. The cherry brandy incident was separate. Some journalists saw him in a pub and it was alleged he was drinking cherry brandy, but he has denied that this was the case.
There was a story about 10 years ago that Prince Andrew was given a birthday caning in a nightclub, but I have no idea of the truth of this.
There have been no reports as to whether Princess Anne was caned though, but I believe that our own Queen was given a spanking as a child by the postman for looking in his bag!