The 50-year-old actor's son Weston Cage and his wife Danielle welcomed a baby boy named Lucian Augustus Coppola Cage on 1 July.
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Nicolas Cage has become a grandfather with the arrival of Weston Cage's baby boy
The new arrival's name honours both his heritage and his ancestry, and was picked out by his parents months before he was born.
"Lucian is of Romanian descent, which is what I am," Danielle told US Magazine at a fundraiser back in February. "And August is taken from Weston's grandfather."
Weston then added, "His name is August. We honour him very much. He was of extreme brilliance. He was a genius."
Weston Cage, his wife Danielle, Alice Kim and Nicolas Cage
The 23-year-old musician, whose mother is Nicolas's ex-girlfriend Christina Fulton, said his father was very much looking forward to the baby’s arrival.
"My dad is ecstatic," he said of the star, who has an eight-year-old son, Kal-El, with his wife of ten years Alice Kim.