Royalty

Andrew Mountbatten-Windsor -- formerly known as Prince Andrew -- turned fun bags into kicks for kids in some very un-princely photos obtained by TMZ.

These pics of Andrew, taken back in 2011, show the then-Duke of York kneeling across from a young boy and rolling a ball back and forth with him.

Just clean, wholesome fun ... until you realize the ball is painted like a breast, complete with a pale pink nipple protruding from it.