How to see $x^6-1=(x^2−1)(x^2+x+1)(x^2−x+1)$?

$x^6-1=(x^3+1)(x^3-1)\\x^3-1=(x-1)(x^2+x+1)\\x^3+1=(x+1)(x^2-x+1)$
might help.

Also, by using your idea we obtain: $$x^6-1=(x^2-1)(x^4+x^2+1)=(x^2-1)(x^4+2x^2+1-x^2)=$$ $$=(x^2-1)((x^2+1)^2-x^2)=(x^2-1)(x^2-x+1)(x^2+x+1).$$