i am trying to find all the integer triples that satisfy

x^3 +y^3 +z^3 =(x+y+z)^3

i got as far as x^3+y^3+z^3=x^3+3x^2y+3y^2z+3x^2z+6xyz+3xy^2+3xz^2 +y^3+3yz^2+z^3

=3x^2y+3y^2z+3x^2z+6xyz+3xy^2+3xz^2+3yz^2

i know that all of the terms are divisible by 3 but i am not sure exactly how to proceed.