They included the song on their first album, but this is a live performance from 1963 on the TV show, Hootenanny, in front of a crowd at Rutgers University.
And hey, as long as we're on the theme and you're marching along, here's the famous "Colonel Bogey March" scene from the movie, The Bridge On the River Kwai -- which the Brothers talk about in their performance. (Don't adjust your volume control, it's quiet at the beginning.)
Oh, heck, while we're at it, let's throw in a bonus. It'll be a long march, after all. In their comic bantering above, the Smothers Brothers talk about Mitch Miller and the sing-a-long gang having a hit record with "The Colonel Bogey March" at the time of the movie -- which is true. No words, just whistling (and a very slight bit of humming). So, for the record (literally...), here it is.