"Lucian Augustus Coppola Cage was born on July 1, 2014 at 3:14 p.m.," the rep tells Us. He is the couple's first child.
News of Danielle's pregnancy first broke earlier this year. Speaking with Us Weekly at the Kasem Cares Foundation fundraiser back in February, the then-parents-to-be lit up while talking about their baby news.
"My dad is ecstatic," Weston, a musician, raved of his famous father, 50, who also has an 8-year-old son, Kal-El, with wife Alice Kim. (Weston is Cage's son with Christina Fulton.) "He was elated immediately when he met Danielle," the rocker added.
The couple also explained their choice of a baby name, which they picked out months before Lucian's birth. "Lucian is of Romanian descent, which is what I am," Danielle told Us. "And Augustus is taken from Weston's grandfather."
"His name is August," Weston piped in. "We honor him very much. He was of extreme brilliance. He was a genius."
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