Yes, Nero is Vergil's Son. There is a mission in Devil May Cry 4 where Agnus trying to put the broken Yamato back together but he can't. Nero arrives at his lab, and a confrontation between Nero and Agnus occurs as Nero trying to find out what's is all going on. Agnus refuses the tell the answers to Nero and stabs him. Agnus called his guards to take the wounded Nero out but suddenly Nero's arms reflects to the broken Yamato and it was putted back together. Nero become more powerful due to the sword. These all scenario proven that Nero is the only one can fix Yamato, which is a sign that Nero is Vergil's son. The last scenario where Dante and Nero defeated the Sanctus and the false Savior. Nero tried to return the Yamato to Dante but Dante refuses to take it. Dante entrust the Yamato to Nero because it was a worth gift for Nero. He also says it's gotta stay in the family. This proves Nero has some sort of blood link to Dante and Vergil.
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Nero
yes cuz in dmc 5 at the end him and the girl was still together so that kid could have been nero in dmc 4 dante looked older than nero.Nero might have been a teen i dont know about his arm though.
Nero (Roman Emperor)
Nero from Devil May Cry 4, from the top of my head.
Goku doesn't have a third son. He only has Gohan his first son and Goten his second son.