Difference of Two Even Powers

Theorem
Let $\mathbb F$ denote one of the standard number systems, that is $\Z$, $\Q$, $\R$ and $\C$.

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Then for all $a, b \in \mathbb F$:

Proof
whence the result.

Also see

 * Factors of Difference of Two Even Powers
 * Difference of Two Odd Powers