The Ghost Rider star's 23-year-old son, Weston Coppola Cage, welcomed a boy with his wife, Danielle, on July 1.
"Lucian Augustus Coppola Cage was born on July 1, 2014 at 3:14 p.m.," the couple's rep told Us Weekly on Thursday.
"My dad is ecstatic. He was elated immediately when he met Danielle," Weston said before the birth.
Weston, a musician and actor, is Nicolas Cage's son with actress Christina Fulton. He has another son, Kal-El Coppola Cage, with his current wife Alice Kim.