Arithmetic Derivative on sum of two perfect squares

Question

Let $n,m \in \mathbb N$ and $n$ even, $m$ odd. If we take there squares and add them $n^2+m^2$, are there examples when we take the arithmetic derivative of the sum:

$(n^2+m^2)' \equiv 0 \mod 4$ ?

Answer 1

$$ 625 = 5^4 = 20^2 + 15^2 $$