How to make a pyramid extruded hole?

You can add draft to the CutExtrude or do a Combine feature with the Subtract option. (model two bodies and subtract the other)

Add Draft to your Cut.

1. Loft cut to a point.
2. Extrude cut with draft.
3. Subtract a solid triangle from your solid you want the hole in.

Take your pick, just make sure your point doesn't end on a surface creating 'zero thickness geometry'.