This is because:
(x+y)(x^2-xy+y^2)= x(x^2-xy+y^2) + y(x^2-xy+y^2)= x^3 - x^2y + xy^2 + yx^2 - y^2x + y^3= x^3 + y^3
This is because:
(x+y)(x^2-xy+y^2)
= x(x^2-xy+y^2) + y(x^2-xy+y^2)
= x^3 - x^2y + xy^2 + yx^2 - y^2x + y^3
= x^3 + y^3