Second cousins.
Your grandson and your brother's grandson are second cousins to each other.
Your grandson is your brother-in-law's great nephew, and your brother-in-law is your grandson's great uncle.
Your brother is a great great uncle to your great grandson. Your great grandson is your brother's great great nephew.
Your grandfather's brother's grandson is your great uncle's grandson. The grandchildren of great aunts and great uncles are your second cousins.
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.
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 great grandson of your great grandfather's brother is your third cousin
Yes, you are related to your brother-in-law's grandson. Your brother-in-law's grandson would be your nephew once removed. This means that you are not directly related by blood, but you share a family connection through your brother-in-law's family.
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.
Nephew?!
The grandson of your great grandmother's brother is second cousin to one of your parents, and your second cousin once removed.