Question 666189
a^6 - b^6 =  (a^3)^2 - (b^3)^2 =  (a^3-b^3)(a^3+b^3) = [(a-b)(a^2+ab+b^2)][(a+b)(a^2-ab+b^2)]

Putting it together a little more nicely we get:

(a+b)(a-b)(aČ+ab+bČ)(aČ-ab+bČ)