Liouville's Extension of Dirichlet Theorem

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Can we use Liouville's Extension of Dirichlet Theorem to find triple integral $\int\int\int(u^2+v^2+w^2)\space du\space dv\space dw\space where\space u=0, v=0, w=0\space \&\space u+v+w\leq1$? Or is it restricted only to functions of the form $F(u+v+z)$?