You and your first cousin's grandson are first cousins, twice removed, to each other.
Your first cousin's grandchild and your grandchild are third cousins.
You and your uncle's grandson are first cousins once removed.
The grandchildren of siblings are second cousins to each other.
Your grandson and your great nephew are second cousins to each other.
Your niece and one of your grandson's parents are first cousins. That makes your niece a first cousin once removed of your grandson.
The grandson of your first cousin and your grandson are third cousins to eachother.
Your grandson and your first cousin are first cousins, twice removed. Your grandson and your second cousin are second cousins, twice removed. and so forth.
A great great grandchild and a great great nephew of the same person are third cousins, once removed.
Your grandson and your first cousin are first cousins, twice removed.
Your grandson and your nephew are first cousins, once removed.
Your grandson and great grand son could be cousins,(first cousins once removed), they could be uncle and nephew, or they could be father and son. It depends on how they are related to your children. If your great grandson is the grandchild on one of your children and your grandson is the child of a different one of your children, they are first cousins, once removed. If your great grandson is the child of a sibling of your grandson, then they are uncle and nephew. But your great grandson could also be the son of your grandson. Then they are father and son
Your niece's child and your grandson's child (your great grandchild) are second cousins, once removed, to each other.
They are cousins.