Add up the first few cubes, and you always land on a perfect square
Try it: 1 cubed + 2 cubed + 3 cubed = 1 + 8 + 27 = 36, and 36 is a perfect square (6 squared). Try it again with more cubes: 1 + 8 + 27 + 64 = 100, also a perfect square (10 squared). Does this pattern — the sum of the first n cubes always landing exactly on a perfect square — keep working forever, no matter how far you extend it?
Reveal the answer
Yes, and it works because of a tidy identity: the sum of the first n cubes always equals the square of the sum of the first n whole numbers. The result appears in the 'Introduction to Arithmetic' by the ancient Greek mathematician Nicomachus of Gerasa around 100 AD, making it one of the oldest recorded number patterns still taught in classrooms nearly 2,000 years later.
— Nicomachus of Gerasa, Introduction to Arithmetic — c. 100 AD