Your grandmother's first cousin's grandson is your third cousin.
Your grandson and your first cousin are first cousins, twice removed.
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.
First cousins
First cousins
Your sister's child and your 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.
Your first cousin's grandson son is your grandson's third cousin. Your second cousin's grandson is your grandson's fourth cousin. Etc., etc.
Your grandson and your sister's grandson are second cousins to each other.
Your daughter's son's son is your great grandson. Your daughter and your sister's son are first cousins. Your great grandson and your sister's son are first cousins, twice removed. Your great grandson and your sister's great grandchild are third cousins.
Your first cousin's grandson is your first cousin twice removed.
Your son and your aunt's child are first cousins, so your son and your aunts grandson (the son of your aunt's child) are first cousins, once removed.