> It's a remake/rendition of a song called 'Mambo Gallego', but I don't think anyone has ever figured out who the artist that did it is.
on us.imdb.com's entry for Mambo Kings, that is credited to Tito Puente. Below is a link to a CDNow.com sample of the song in question.

• Sample's from a Tito Puente greatest hits CD