The surface area of each face of a sugar cube is 1*1 = 1 units²
The rectangular box has 6 faces in contact with sugar cubes. The area of each of two faces is 18*6 = 108 units² Therefore these two faces touch 2*108 = 216 cubes
There are two other faces each of area 18*8 = 144 units² Therefore these two faces touch 288 cubes.
There are another two faces, each of area 6*8 = 48 units². Therefore these faces touch 96 cubes.
The total number of cubes touching the faces of the box are 216 + 288 + 96 = 600
