Actually, those songs (except maybe numbers? Have not seen...) are more like children's songs. You know? There are a lot of kids' songs haha...
This is a flash from Korean site..:
아기 돼지 엄마 돼지 (Baby Pig Mommy Pig)
Korean lyrics are on the video^^
Famous song, maybe? :P I have it on a video of Korean children's songs... LOL
I know there are other popular ones...!
EDIT: Oh~~I remember one. But maybe you don't like this... (It's sooo famous nowadays because it was in 'Full House' :P)
곰 세 마리 (Three Bears)
There are lots of different video versions for this song. This one is really cute, though...
(Also with Korean lyrics on the video^^)
There are so many newer Korean children's songs now, too! Even a 라면 송 (Ramyun Song) lol
Kinda like an oldies rap/ballad HAHA
라면 송 (Ramyun Song)
Please enjoy^^
You can find many others on YouTube, too if you are looking at these kinds of songs...
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In addition, I wanted to make a note about the Carrot Song (당근 쏭). If you have ever watched the variety show <X-man (X맨)> on YT or somewhere, then you have probably seen the portion called "당연하지 (Dangyunhaji AKA "Of Course"). You can also say 당근이지 (Dang-geun-ee-ji) which is also meaning "Of Course." But it's sort of a play on words here, I think, because 당근 means carrot, but it can also mean "of course" so when in the song it is saying "do you love me? do you like me?" etc. etc. the carrot is saying "of course!" (Maybe I'm thinking wrong...LOL)
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One more thing... As far as being "educational" videos, I think that mostly the videos (like the milk song and egg song) are just trying to get kids to eat those things so they can grow and be healthy xD So just saying instead of drinking soda, drink milk! And eggs have protein and are good for you... haha...^^ Korean songs are silly~