And if the contents of any two of the boxes were united they would form a square number.
In fact, the sum of any number of consecutive cubes, beginning always with 1, is in every case a square number.
Any square number may be expressed as the sum of two squares in an infinite number of different ways.
Then came the further order, "All pyramids are to contain a square number of balls."
An exact numerical measurement can only be obtained when the sum of the squares of the two sides is a square number.