Angular Momentum in Quantum Mechanics

Why the square pyramidal number formula is interesting? (It is just the formula for the sum of squares of the natural numbers which happens also to give the number of cannon balls or oranges of equal size in a pyramid with a square base.) It can be used in the derivation of the expected value of angular momentum in Quantum Mechanics.
www.avidsynergy.com/pdf/angular_momentum_in_QM.pdf