question
Show that the number $$\frac{\sqrt{2021^4+2 \cdot 2020^2-4041^2}}{505 \cdot 1011}$$ is natural and a perfect cube.
my idea
I tried writing the upper part as a perfect square so that we could get rid of the radical.
I tried using these formulas
$$(a+b)^2=a^2+2ab+b^2$$
or
$$(a-b)^2=a^2-2ab+b^2$$
but could not get anywhere useful.
I also tried writing $4041^2=(2020+2021)^2$
I don't know where to start. I hope one of you can help me! Thank you!