The points on your cubical planet (or triangular) would be tall mountains that would be crushed under their own weight and flattened.
Gravity tends to pull matter into spherical shapes. The strength of the materials resist this pulling. If a body is large enough (a planet), then gravity becomes strong enough to overcome the properties of the materials.
Earth is not a perfect sphere, though, because of the gravity of the Moon and Sun. Earth is considered to be an oblate spheroid.