The walls of the hollow block should be one cube thick in order to use the fewest number of cubes possible. Thinking about this, we first build the floor of the cube which is 5 cubes by 5 cubes (totaling 25 cubes). Next we build the ceiling of the block which is also 5 by 5 cubes (again 25 cubes). To build the four walls we will have to count the number of cubes around the edges of the ceiling of the large block. There are 16 blocks around the edges and we observe that the four walls need to be three cubes high (not including the floor or ceiling). The number of cubes in the four walls is 16 x 3 = 48 cubes. So, the hollow block has 25 + 25 + 48 = 98 cubes.
One way we can find the greatest number of cubes that can fit inside the hollow space is to imagine a solid block with 5 cubes on each edge. If we take away the outer cubes we are left with a block the size of the hollow space. This block has 3 cubes on each edge so it has 3 x 3 x 3 = 27 cubes.
