By Jen Juneau
July 20, 2017 at 04:17 PM EDT
Credit: Robin Marchant/Getty Images

Joseph Gordon-Levitt’s life just got a little sunnier!

The Snowden star and his wife, businesswoman and robotics expert Tasha McCauley, are second-time parents to a baby boy they welcomed in June, a rep confirms to PEOPLE. No other details, including the baby’s name, are available.

McCauley and Gordon-Levitt, 36, share another son, who turns 2 next month.

A rep confirmed the news of Gordon-Levitt and McCauley’s second child on the way to PEOPLE in May. Of the couple’s relationship, the actor told Howard Stern in 2013 that he doesn’t “really like to talk about it in public.”

“The girl that I’m with, she really doesn’t want to be a part of that,” Gordon-Levitt admitted of McCauley, who earned her bachelor’s degree in robotics and an MBA in business education and research.

During a 2015 interview on Live! With Kelly and Michael, the 3rd Rock from the Sun alum explained that his career and in-the-spotlight status was a choice he made — and that he wants to afford his son that same decision.

“My son … he hasn’t made the choice to be in the public eye, and that’s a choice that I would like him to be able to make when he’s older, when he can think about these kinds of things and make that decision for himself,” said Gordon-Levitt.

“So, for now, I’m just a protective dad, and I want to protect his privacy,” he added.

  • Reporting by JULIE JORDAN

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