Échame la culpa is a classic Spanish phrase that literally means "Throw the blame on me." It's a dramatic and very common way to say "Blame me" or "Put the blame on me."
In this iconic song, the singer selflessly tells his unfaithful ex-lover to blame him for everything that went wrong. It's a powerful statement of martyrdom, where he offers to take all the fault (la culpa) to protect her reputation, capturing the song's deep sense of heartbreak and chivalry.
This song is one of the most dramatic breakup songs you'll ever hear. The singer has been cheated on, and he knows it. He tells his ex, "Sabes a ciencia cierta que me engañaste" (You know for a fact that you cheated on me). But instead of getting angry, he does something completely over-the-top.
He decides to take all the blame to protect her. He literally tells her, "Échame a mí la culpa de lo que pase" (Blame me for what happens). He wants her to tell everyone that he was the one who was awful, so she can "cúbrete tú la espalda con mi dolor" (cover your back with my pain). He even wishes her a good afterlife, hoping she finds glory instead of hell and that a cloud erases him from her memory. It's a grand, self-sacrificing gesture from someone who has been deeply wronged.