#math trivia for #September21: #264 is the sum of a square and a cube, and also of two squares and a cube. What are they?

— Burt Kaliski Jr. (@modulomathy) September 22, 2013

Answer: The square and cube are 256 = 16^{2} and 8 = 2^{3}.

The two squares and cube are 4 = 2^{2}, 196 = 14^{2}, and 64 = 4^{3}; or 100 = 10^{2}, 100, and 64. (Or, trivially adapting the first answer, 0, 256 and 8.)

(For simplicity, I’ve assumed the cubes are positive; it would be interesting to see if allowing negative cubes — and thus potentially much larger squares — would yield further solutions.)