Cobre literally means "copper." While it might seem like an ordinary word, in this song, it's part of a very common and interesting Spanish idiom: "enseñar el cobre."
"Enseñar el cobre" means to show one's true colors, often revealing a negative or unpleasant side of someone's character. The lyrics "No vales la pena porque ya enseñaste el cobre" (You're not worth it because you've already shown your true colors) use this phrase to powerfully convey the speaker's disillusionment with a past lover.
This song is all about getting over a breakup, and the singer is done with feeling bad! He's making a big promise to himself, saying "Cuánto a que te olvido" [How much do you bet I forget you?]. It's like he's challenging himself, and maybe even his ex, that he's going to move on.
He's pretty confident, too, declaring "No creo que me duelas más de lo que me ha dolido" [I don't think you'll hurt me more than I've already been hurt]. He's even a little sassy, saying "Cuando menos pienses, vivirás en el olvido" [When you least expect it, you'll live in oblivion]. He feels his ex doesn't deserve his thoughts, because they've "enseñaste el cobre" [showed their true colors]. He's determined to be brave and not give in, even if he has to "morderme un dedo pa' no verte" [bite my finger to keep from seeing you]. He's serious about this, even mentioning, "Esta es la tercera peda donde no te llamo" [This is the third drunk night where I haven't called you] – so you know it's real! He's so sure, he even bets, "Cuánto a que me ruegas" [How much do you bet you'll beg me?]. Talk about moving on with confidence!