A cube of volume 27 has 1 x 1 square holes drilled through the center of each face and passing through the center of the cube. What is the volume of the

The total volume is 27 so each side has length 3. Boring a single hole through the cube removes a region of size , so removes a volume of 3, however these volumes overlap in the center  region of the cube.

The first hole drilled removes a volume of 3. The second and third hole drilled only remove a volume of 2, so the total resulting volume is
27-3-2-2=20

so your answer is 20