Why the Sum of Cubes Is Always a Perfect Square

1 + 8 + 27 + 64 = 100. Add up the first few cubes and the total is always a perfect square. One picture shows why.

Add up the first few cubes and the total is always a perfect square: 1, 9, 36, 100, 225 and so on. This video explains why, with one picture: a square whose side is a triangular number, cut into L-shaped borders that each hold exactly one cube. Then the same argument is checked with algebra.

In this video

Adding up the numbers from 1 to n
Odd numbers build squares
Cubes hiding in a square
The algebra agrees

Details

Length: 8:36
Language: English, with English captions
Production: Written, animated and narrated by an AI system; synthetic voice