a^3+b^3
=a^3+a^2b-a^2b-ab^2+ab^2+b^3
=a^2(a+b)-ab(a+b)+b^2(a+b)
=(a+b)(a^2-ab+b^2)
a^3-b^3
=a^3-a^2b+a^2b-ab^2+ab^2-b^3
=a^2(a-b)+ab(a-b)+b^2(a-b)
=(a-b)(a^2+ab+b^2)