Here is a clip of the Spanish Children's song
My cousin started singing it, but he made up words. However, the melody sounded vaguely familiar, so I sang along.
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Oddly, this song has a very interesting history. The title in Spain is "Arrorró mi niño". If you Google the title along with the name Francisco García-Talavera, you will find several versions of an interview that researcher gave about the song.
Long story short, it is originally a lullaby of the Berber people, and Spain picked it up when they were under Islamic rule.
In Mexico people sing "Duérmete mi niño" to the same tune.