That's easy one !!! 3

Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations: 3x − y − z = 0 , − 3x + z = 0 , −3x + 2y +z = 0,Then the number of such points for which, ${ x }_{ }^{ 2 }+y{ }_{ }^{ 2 }+z{ }_{ }^{ 2 }\le 100$ .Let the number of points be 'n', then find $(n+10){ }_{ }^{ 3 }$ .