Well, this is true?
Uncle Cecil covered this in More of the Straight Dope, which is available at bookstores everywhere. And, as he says in Did Hitler have only one testicle?, there is some evidence that the song was true.
All the bookstores everywhere IN THE USA :D, but if the book can be bought online, then I’ll do it. I love this stuff.
And all these years I thought the second line was
“Goering has two, but they are small”
…and it should be “and Doktor Goebbels has no balls at all.”
That’s a version from the comic book miniseries Adventures of the Rifle Brigade. Of course, there must be different versions.