Your great-grandmother's first cousin's grandson is your third cousin once removed.
The grandson of your first cousin and your grandson are third cousins to eachother.
Your grandson and your nephew are first cousins, once removed.
First cousins twice 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 granddaughter and your first cousin's grandson are third cousins to each other. You find their common ancestor that is, your grand parents, and count the number of generations separating them, there are Brother and Sister then cousins, you and your cousin would be one (first cousins), your children and your cousins children are second cousins and their children are third cousins and so on.
You and your great aunt's grandson are second cousins. Your great aunt was the sibling of one of your grand parents, so your parent and your great aunt's child were first cousins. You and the grandson are members of the next generation and therefore second cousins.
Your niece and one of your grandson's parents are first cousins. That makes your niece a first cousin once removed of your grandson.
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.
Your grandson and your first cousin are first cousins, twice removed.
You and your first cousin's grandson are first cousins, twice removed, to each other.
You and your uncle's grandson are first cousins once removed.
Your niece's child and your grandson's child (your great grandchild) are second cousins, once removed, to each other.