Sum of Integers Squared: Math Direct Proof Example

A Direct Proof Example is presented in this video to prove the closed form formula for the sum of the squares of positive integers from 1 to n.
In logic and mathematics, a direct proof is a method of proving statements of the form p ⇒ q ”if p then q” that takes an original hypothesis or assumption p, which we assume to be true, and use it to show directly that the desired conclusion q is true.

[wafikiri_]

It is easy to imagine a geometric interpretation of each side of the proven equality, but to imagine how to fit both sides together is not so easy. Sometimes I've watched cute animations on other similar equalities, arranging rows, squares, and cubes. Surely this one would be challenging but not impossible, and the key to doing it is precisely the mathematical operations you've displayed, for increasing n from one on. Six times s gets rid of fractions, therefore the animation could start with two cubes, three squares, and one line and end in six sets of progressively larger squares as we move things around.