I just happened on this thread while searching for the rest of a song I learned at a stag talent show in college back in late '60 or '61. It went:

My cunt, my cunt, my country's calling me,
A sol, a sol, a soldier I will be.

Two pis, two pis, two pistols by my side,
A hor, a hor, a horsey I will ride.

Fu cu, fu cu, fu curiosity,

and that's all I remember.

It seems like there were at least six or possibly eight lines, and I don't remember a chorus at all. Several lines in the responses above would fit for the last line, but none strike me as being what I heard. I was 18 and in school in Maryland at the time. Also from the responses above I'm getting the impression that this song may have originated with the British Army rather early in the occupation of India and not in the US. Interesting.