The video she posted along with the comment is of two hare's boxing, which you can watch at:So, leaving no stone unturned, note the image at right taken from the "Pat-a-cake, pat-a-cake, baker's man" wiki page. Note as well the name of the illustrator, now note from his wiki page:
William Wallace Denslow illustrations for Pat-a-cake,
pat-a-cake, baker's man,
from a 1901 edition of Mother Goose
https://m.youtube.com/watch?v=s_IwHrRLoMc. It does look a bit like the two hare's are playing a game of "patty cake", hence the caption re "Patty cake Patty cake bakers man...", that in turn connects in cryptic fashion to the name "Patty Duke".
He and Patty Duke died on the same day 101 years apart!!
- William Wallace "W. W." Denslow (May 5, 1856 – March 29, 1915)