In the past I've translated songs with a couple or a mountain of references, some of these references were so obscure that I had to consult others who had a better understanding of what I was looking for. I don't think you'd need to pick up on these things if you didn't know about them or the language, however; there's something quite indescribable when it suddenly "clicks" and you understand them. Here are some examples:
The traditional song "La Sandunga" accompanying a poem by Luis Martínez Hinojosa that depicts Zapotec culture and long history.
A Oaxacan tradition of "stealing the bride" that wouldn't make sense to outsiders (although I think I've heard of it outside of Oaxaca)
About the Aztec culture (and many Nahuatl terms) and the retelling of the appearance of the Virgin of Guadalupe.
A song about Zapotec wedding traditions
So share some of your translations or translations others have made that have taught you a thing or two. I personally love these songs because I'm not opposed to learning something new or if it encourages me to crack a book open to look up on events in history or figures of the past. I also like the hard work that comes with appreciating songs and giving them a well deserved translation. It bothers me sometimes when others take no consideration for the weight in the lyrics and disregard adding anything that might provide readers a better insight on the song.