Madrugadas refers to the very early hours of the morning, typically before dawn. While it literally means "early mornings," it carries a more poetic and intimate connotation than a simple time of day.
In this song, the artist uses "tantas madrugadas" (so many early mornings) to evoke a sense of shared, intimate time spent with a loved one, suggesting deep connection and cherished memories that extend into the quietest hours of the night.
El Komander brings us a song about a love that's hard to forget, even when you're alone. He imagines his former love feeling lonely and missing his kisses, remembering all their beautiful moments together: "tantas madrugadas, tanto beso a solas, alto cariñito, tanto amor bonito, tanto amor de sobra" [so many early mornings, so many kisses alone, so much affection, so much beautiful love, so much love to spare]. It sounds like they had a truly passionate connection, where they'd end up "cansados por tantas caricias" [tired from so many caresses].
He's still thinking about her constantly, even when he's out late. He can't see her anymore, and it's impossible for him to forget her. He even thinks about how she might try to call him, but he won't answer. It's a bittersweet look back at a love that was once everything to him, and now, even though they're apart, her memory is still very much alive.