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

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

(a+b)^3=(a+b)^2*(a+b)

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

=a^3+2a^2b+ab^2+a^2b+2ab^2+b^3

=a^3+3a^2b+3ab^2+b^3

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