A sealed rectangle or box measuring 8*6*18 contains 864 sugar cubes each measuring 1*1*1. How many sugar cubes are touching the box

Since the rectangular box is sealed; the cubes touch the 6 sides of the cuboid.

Total number of cubes that touches the inner surfaces of the box are:

2 (18 * 8) + 2 (8 * 6) + 2 (18 * 6)

288 + 96 + 216 = 600 cubes.