a^3-b^3
=a^3-a^2*b-b^3+a^2*b
=a^2(a-b)+b(a^2-b^2)
=a^2(a-b)+b(a+b)(a-b)
=(a-b)[a^2+b(a+b)]
=(a-b)(a^2+ab+b^2)
=(a-b)(a-b)^2
=(a-b)^3