# Difference between 2 Consecutive Cubes is Odd/Proof 2

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## Theorem

Let $a$ and $b$ be consecutive integers.

Then $b^3 - a^3$ is odd.

## Proof

Let $a, b \in \Z$ such that $b = a + 1$.

Either:

or:

Hence from Parity of Integer equals Parity of Positive Power either:

or:

The result follows.

$\blacksquare$