Next time, please post thy questions in a new thread.Originally Posted bya4swe

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We note that,

Let S represent all N such that it is true.

We know that .

Assume, , i.e. that it is true for k.

Then,

Multiply by 3,

Note that,

For

Add to both sides,

Gaze upon ye perfect cubical,

Transitivity,

Thus,

Thus, S contain all N, i.e. true for all integers.