To simplify the expressions, we can expand the brackets and combine like terms.

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

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