x^3+y^3+z^3
=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)+3xyz
=(x+y+z)((x+y+z)^2-3(xy+yz+zx))+3xyz
=27-9(xy+yz+zx)+3xyz
=27

1/x+/y+1/z=1/3
-9(xy+yz+zx)=-3xyz