A wooden cube with edge length n units (where n is an integer >2) is painted black all over. By slices parallel to its faces, the cube is cut into n3 smaller cubes each of unit length. If the number of smaller cubes with just one face painted black is equal to the number of smaller cubes completely free of paint, what is n?
<spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>7<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>none of these