WOLFRAM|DEMONSTRATIONS PROJECT

Fry's Geometric Demonstration of the Sum of Cubes

​
n
2
3
4
5
step
1
2
The sum of the first
n
cubes is given by the remarkable identity
3
1
+
3
2
+…+
3
n
=
2
(1+2+…+n)
=
2
2
n
(n+1)
4
.
Fry [1, 2] gave a geometrical proof of this result based on the slicing of
k×k×k
cubes into
k
k×k
square slabs and their assembly into a
n(n+1)
2
×
n(n+1)
2
square. For an even summand, one of the square slabs is cut in half for each end of the L-shape.