(x+y+z)^3
=[(x+y)+z]^3
=(x+y)^3+3(x+y)^2z+3(x+y)z^2+z^3
=x^3+3x^2y+3xy^2+y^3+3(x^2+2xy+y^2)z+3xz^2+3yz^2+z^3
=x^3+y^3+z^3+3xy^2+3xz^2+3x^2y+3yz^2+3x^2z+3y^2z+6xyz.