Thanks Q & Masato.
Somewhat off topic:
If been wondering: Is the custom of singing cumulative songs like "Bought me a cat", "There's a hole in the bucket, and "There's a hole in the bottom of the sea" part of other folk tradition besides the English & other European nations? I take it all three of those songs I listed are of European origin, right?

There are some African folktales that have a cumulative element...
For instance, there's a Caldecott Award winning children's book by Verna Aardema there's a retelling of the Africn folktale "Why Mosquitoes Buzz In People's Ears"Dail Books For Young Readers, 1979?}. Here's one excerpt from that story:

"King Lion called th python, who came slitjering, wasawusu, wasawusu, past the other animals. "But King", he cried, "It was iguana's fault ! He wouldn't speak to me. And I thought he was plotting some mischief against me. When I crawled into the rabbit's hole, I was only tring to hide.".
The king said to the council:
"So it was iguana
who frightened the python,
who scared the rabbit,'who startled the crow,
who alarmed the monkey,
who killed the owlet-
and now Mother Owl won't wake the sun
so that the day can come."

end of quote
---
It turns out that the mosquito had told the iguana a big lie and so the iguana put sticks in his ears and frightened the python who scared the rabbit who startled the crow etc. The animals declared that the mosquito needed to be punished, but the mosquito hid because she had a guilty conscience. And to this day she buzzes in people;s ears, whining "Is everyone still angry with me?"

Does anyone know if there are any African folk songs that are cumulative?