I'd love to share "Yogi was a big brown bear", but that one gets really bad after the first few verses.
A little bird, with yellow bill.......
Not a cadence, but- 1. Let Bacchus' sons be not dismayed. . . From Garryowen in glory. And the tune is http://www.contemplator.com/midimusic/garryown.mid When its used as a marching song, like cadence, the leader (senior NCO or Officer) sings the verses, and the unit sings back the chorus.Nearly everyone has heard the song, but most don't realize what it is. For example, its the one tune most people recall from the John Wayne movie The Quiet Man