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Tony-winner David Alvarez can sing, play classical piano, speak three languages and he doesn’t just dance ballet, he is often referred to at the next Mikhail Baryshnikov.

And despite the fact that several times a week, he makes audiences swoon with his outstanding portrayal of Billy Elliot in the award-winning Broadway show, the 15-year-old hasn’t a clue why he was cast in the musical.

“No, I still don’t understand why,” says a modest Alvarez.

It’s not that the teen lacks confidence, far from it. He is a modern-day Renaissance manchild and he knows it.

For this interview, he has chosen to speak Spanish but he switches back and forth between that and English, fluidly and with eloquence. (He also speaks French.)

“A bunch of people [from American Ballet Theater] have said that I can be the next Baryshnikov and when they say that, I know that there’s much work ahead of me. To be that good, you have work very hard,” he says.

It’s this kind of focus, discipline and maturity that got Alvarez, who grew up in San Diego with his two sisters and a stay-a-home mom and biochemist-professor dad from central Cuba, noticed by casting directors.

Show insiders say that he is a perfectionist, wanting to get everything just right. And when, every once in a blue moon, he doesn’t, he turns his anger inward.

“I just can’t help it— but I am trying to get better at not being so hard on myself,” says the soft-spoken young star.

Alvarez was a four-foot tall cherubic boy when he first started playing Billy, a little English boy from a working-class mining town who has dreams of dancing ballet. Today, he is in full-blown adolescence and those awkward growth spurts are happening on the set and behind the scenes.

“I grew 5 inches from the first day I started playing him,” he says. “One morning I woke up and said ‘Whoa, what happened?’” he says, chuckling.

Every so often, he admits, his voice cracks on stage.

“I have learned to work my way around that, it’s a little embarrassing,” he admits.

Young Alvarez says he’s already planning his future, post-“Billy.”

“I will go to ABT full-time to study ballet,” he says. He now studies at the prestigious school on scholarship while not performing.

He’s also studying classical piano on full scholarship at the 92 Street Y.

“The piano helps me tremendously with the musicality of ballet.”

But Alvarez’s plans don’t end there.

“I also want to do films, something very Hollywood.”

In fact, he says he auditioned for a couple of movies that he’s excited about, but not ready to reveal.

And if all this doesn’t work out, Alvarez — who is a voracious reader of war books and films — says he wouldn’t mind enlisting in the army.

“There is something that I really love about the military — maybe it’s the discipline.”

Catch David Alvarez in “Billy Elliot” currently on Broadway.