# I lie on U

A cube $$U$$ in $$\mathbb{R^3}$$ has its vertices at $$(0,0,0)$$, $$(8,0,0)$$, $$(0,8,0)$$, $$(0,0,8)$$, $$(8,8,0)$$, $$(8,0,8)$$, $$(0,8,8)$$, and $$(8,8,8).$$ How many lattice points lie on the surface of $$U$$?

Details and assumptions

A lattice point has integer coordinates.

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