Mathematics · Permutations and Combinations

A large cube of size 4 × 4 × 4 is constructed using 64 small identical cubes. One insect attacks one corner of the large cube and eats all small cubes diagonally through to the opposite corner. Remaining three insects attack one small cube each on three different outer surfaces of the large cube and each eats a straight line of cubes through that respective layer. If none of the paths intersect except at already eaten spaces, and a total of 14 distinct small cubes are eaten, how many small cubes remain completely untouched?