Lucas has been looking at extensions of the painted cube problem. He is starting with a 5-unit cube and has decided to paint three adjacent faces black and the three other faces gold. After the paint dried he carefully cut the cube into 1-unit cubes. How many 1-unit cubes will there be? How will they all be painted? For example, how many 1-unit cubes will have 3 faces painted black? How many cubes will have two faces painted black and no other faces painted? What other color combinations are there for the cubes? Use good problem-solving strategies to make generalizations for the results of an n-unit cube.