题意即要求证X^3+Y^3+Z^3-3XYZ=0
证明如下：x^3+y^3+z^3-3xyz =（x+y+z)(x^2+y^2+z^2-xy-yz-zx)
因为X+Y+Z=0,所以上式等于0.所以x^3+y^3+z^3-3xyz=0,X^3+Y^3+Z^3=3XYZ,得证.