Nicomachus's theorem states that
, where
is a positive integer. In words, the sum of the cubes from 1 to
is equal to the square of the sum from 1 to
.
For a visual proof, calculate the total area in the figure in two different ways: First, count the unit squares from the center to an edge to get
, so that the total area is
. Second, consider that each square ring consists of
squares of side
, with area
.
