Depending on whether you are a member of the older or younger generation in the relationship, the grandson of your first cousin three times removed is either:
Your grandson and your first cousin are first cousins, twice removed.
Your first cousin's grandson is your first cousin twice removed.
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.
The grandson of your father's first cousin is your second cousin once removed.
Your first cousin's grandson is your first cousin twice removed. Your second cousin's grandson is your second cousin twice removed. Your third cousin's grandson is your third cousin twice removed. And so forth. If your cousin is once removed, twice removed, etc., the relationship possibilities for you and the grandson become more varied and complex.
Your great grandmother's first cousin's grandson is your third cousin once removed
Your aunt's grandson is the son of your First Cousin and is therefore your First Cousin once removed Ref: http://freepages.genealogy.rootsweb.ancestry.com/~gentutor/chart.html
Your first cousin's grandson is your first cousin, twice removed. Your second cousin's grandson is your second cousin, twice removed.
Your grandson's third cousin is your first cousin twice removed, and you are hers. You count from the cousin who is closest in generation to the common ancestor in determining what kind of cousin relationship applies.
Your aunt's great grandson is your first cousin twice removed.
Your cousin's child is your "first cousin once removed". If you were to have children, your child and your cousin's child would be second cousins. The son of your cousin's son would be your first cousin twice removed. Look at it like this: you * your cousin * ** your cousin's son (your cousin once removed) ** *** your cousin's grandson (your cousin 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.