You know I once thought that Nero was a son of Sparda. Or perhaps, the son of Dante/Vergil. This was before I looked into it and realised that it wouldn't work out and that it was illogical. Now I don't think he is a son of Sparda, or Dante/Vergil's son. I don't think he is a son of a third son of Sparda. A son that neither of the twins knew about. My reasoning is this, however. Obviously I have to have a point in why I think the way I do. This isn't to go against anyone else's opinion.
In my opinion, Sparda didn't have a third son that we didn't know about. Why? Because he loved Eva. He fell in love with her. It was this love that helped him find the strength to rebel against his own kind. Her love that taught him how to truly feel for things. Her love almost made him human. And after living in the human World for so long and giving up his own demonic powers, sacrificing that power, he became more human than he ever was before. Sparda made a family with Eva. We're unsure of what happened to him, but we know that she was killed and Dante and Vergil were left without a mother or a father. But in my honest opinion, from all in which Sparda gave for his love for Eva, I don't think he would of been able to find it in himself to make love to another woman.
Unless you're talking about him having the third kid with Eva. Then in that case, where was he/she when Dante and Vergil were eight years old?