GoForSmoke:
40-some years ago you could buy a square hole drill for wood that had 4 chisels with a drill in the middle. The chisels cut the square and the drill removed the wood in the center.
You're describing a "mortising bit" (just the bit) or "mortiser" (full machine). Any woodworking store would have them and the machines are still widely sold. To use a mortising bit with a drill press you'd need a "mortising attachment" (~$100).