Mikkel: How are you? For a hole that size (which I would not suggest but) you may have a gouge that will work, even a narrow chisel will do. If all else fails I have a three inch hand auger but the shipping would be prohibitive. Trust all is well, Curtis
I suspect your hole has since been made - but here's a yankee solution; Try using a regular hole saw and a chisel. The hole saw should get you about 1 1/2 to 2" in before your have to stop and use the chisel to clear out the core. Repeat till done - just keep yourself lined up. With the extensions that are usually available you should be able to go 16" deep without much problem. You could also use a slick to knock pieces loose. Not the most elegant solution but it gets the job done.