Peg-in-Cube Puzzle

This puzzle consists of a perforated cube and 42 pegs of different lengths.

Description
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The holes create 125 internal volumetric units within the cube. Depending on its length, a peg closes off two, three, or four of these units. There are 14 pegs each of lengths two, three, and four. This totals a volume of 126 volumetric units. Therefore, it is not possible to insert all 42 pegs into the cube. In the best-case scenario, one peg of length two will remain.

The holes and pegs are designed with a slight taper. With a little pressure, the peg can be secured in the cube so it doesn't fall out immediately.

The pegs are usually printed in different colors so that one can see how many units they occupy. The first picture shows the cube with white pegs of length two, blue pegs of length three, and red pegs of length four.

To increase the difficulty of the puzzle, all pegs can also be printed in the same color. The second picture shows the cube and all 42 pegs in the same co