# Fry's Geometric Demonstration of the Sum of Cubes

Fry's Geometric Demonstration of the Sum of Cubes

The sum of the first cubes is given by the remarkable identity

n

3

1

3

2

3

n

2

(1+2+…+n)

2

2

n

4

Fry [1, 2] gave a geometrical proof of this result based on the slicing of cubes into square slabs and their assembly into a × square. For an even summand, one of the square slabs is cut in half for each end of the L-shape.

k×k×k

k

k×k

n(n+1)

2

n(n+1)

2