Since we know that 27 cubes do not have paint on any face, we can assume that those 27 cubes make up the interior of the cube.
A cube has 3 dimensions, so take the cubic root of 27:
This let's us know that 3 cubes make up the length, width, and height of the interior.
To add the outside cubes, add 2 to the length, width, and height (which makes the dimensions 5 x 5 x 5.
Lastly, find the volume with these new measurements: