Do you know this one?

[Whateverist]

SPOILER ALERT: Okay and here is my much cruder argument.

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Let n = any odd number, 3 or greater.

Once you remove the stack of 1 by 1 by n from the original cube, what is left could be decomposed into two pieces.

The 1 by n by n slice from which the one stack was removed now has dimensions: n by n – 1 by 1.

The larger piece is n by n by n – 1.

If these two remaining pieces are joined by their n by n – 1 sides, the resulting object would be prism with dimensions: n + 1 by n by n – 1.

Since n – 1, n and n + 1 are three consecutive counting numbers, one of them must be a multiple of 3.

n – 1 and n + 1 are two consecutive even numbers. Since every other even number is a multiple of four, one of the dimensions must be a multiple of 4 while the other is a multiple of 2.

Since the object's dimensions contain multiples of 3, 2 and 4 it is also a multiple of 24, hence divisibility by 24.

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