You have an attention grabber by stating "One can even drill square holes."

and later you state with emphasis "No - you can't drill square holes" so I rectify it for you.

All you need is a drill bit, an almost stock standard round drill bit !!

Make sure it has 90 degrees cone at the bottom.

1. Take a piece of shim, fold it in half.
2. Clamp it in a vice edge wise
3. Drill a hole no deeper than the height of the cone

Take the shim out of the vice, unfold ...

Square hole with sharp corners with a round drill bit no less !!

Giorgis
giorgis.3erolas@gmail.com