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 \((n+10){ }_{ }^{ 3 }\).

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