Your brother is a great great uncle to your great grandson. Your great grandson is your brother's great great nephew.
Your grandson is your brother-in-law's great nephew, and your brother-in-law is your grandson's great uncle.
Your great grandmother's brother's great grandson is your third cousin.
Your brother's grandson is your great nephew and you are his great uncle if you are a man, or great aunt if you are a woman.
The grandson of your great grandmother's brother is second cousin to one of your parents, and your second cousin once removed.
Your brother is your grandson's great uncle, and your grandson is your borther's great nephew. Some people would also say grand nephew and grand uncle.
second cousin/once removed
Your grandson is the great-nephew of your brother.
Your grandson and your brother's grandson are second cousins to each other.
Your grandmother's brother is your great uncle. You and your great uncle's grandchild are second cousins to each other. Your and your great uncle's great grandson are second cousins, once removed.
Your grandfather's brother's grandson is your great uncle's grandson. The grandchildren of great aunts and great uncles are your second cousins.
The great grandson of your great grandfather's brother is your third cousin
Your brother-in-law is your spouse's brother. His grandson s your spouce's great nephew. (Some people say grand nephew). That makes him your great nephew, too. Your brother-in-law could also be the husband of your sister. Then your brother-in-law's grandson is your sister's grandson and your great nephew.