Your nephew's great grandson is your great great great nephew and you are his great great great aunt (if you are a woman) or great great great uncle (if you are a man).
You are their great aunt/uncle.
You are your nephew's aunt/uncle,,, his children are your grandnieces/nephews,, his grandson is your great-grandnephew.
The son of your grandson is your great grandson. You are his great grandmother or great grandfather.
Your father's great grandson could be your grandson, or your great nephew.
Your brother is a great great uncle to your great grandson. Your great grandson is your brother's great great nephew.
You Aunt is you grandson's Great-Great Aunt. Your grandson is your Aunt's Great-Great Nephew.
You grandson is great great nephew to your uncle. You uncle is great great uncle to your grandson
You grandson is great great nephew to your uncle. You uncle is great great uncle to your grandson
They are your grand-nephews and grand-nieces or great-nephews and great-nieces.
Your nephew's children are your great nephews and great nieces (or grand nephews and grand nieces).
You and your great great aunt's great grandson are third cousins.
George Washington's great great grandson did not go to school. Washington had no children of his own so he had no great great grandson.