The original $5 \times 5 \times 5$ cube has 6 faces, each of which is $5 \times 5$. When the three central columns of cubes is removed, one of the '1 \times 1$squares' on each face is removed. This means that the surface area of each face is reduced by 1 to$5 \times 5 - 1 = 24$. This means that the total exterior surface area of the cube is$6 \times 24 = 144$. When each of the central columns is removed, it creates a 'tube' that is 5 unit cubes long. Each of these tubes is$5 \times 1 \times 1$. Since the centre cube of the original$5 \times 5 \times 5$cube is removed when each of the three central columns is removed, this means that each of the three$5 \times 1 \times 1$tubes is split into two$2 \times 1 \times 1$tubes. The interior surface area of each of these tubes consists of four faces, each of which is$2 \times 1$. (We could instead think about the exterior surface area of a$2 \times 1 \times 1$rectangular prism, ignoring its square ends.) Thus, the interior surface area from 6 tubes each with 4 faces measuring$2 \times 1$gives a total area of$6 \times 4 \times 2 \times 1 = 48$. In total, the surface area of the resulting solid is$144 + 48 = 192$.