Difference between 2 Consecutive Cubes is Odd/Proof 1

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

Then:

From Product of Consecutive Integers is Even, $a \paren {a + 1}$ is even.

Hence $3 a \paren {a + 1} + 1$ is odd.

Hence the result.