How do you factor x^6-y^6

start by looking at it as as difference of squares:
x^6 - y ^6 = (x^3 + y^3)*(x^3 - y^3)
then (x^3 - y^3) = (x-y)(x^2 + xy +y^2)
so...
(x-y)(x^2 + xy + y^2)(x^3 + y^3)
then look at x^3 + y^3 = (x+y)(x^2 - yx + y^2)
so...
(x-y)(x+y)(x^2 +xy + y^2)(x^2 - xy + y^2)

x^6 - y^6
= (x^2)^3 - (y^2)^3
= a^3 - b^3
= (a - b)(a^2 + ab + b^2)
= (x^2 - y^2)(x^4 + x^2y^2 + y^4)