Would Gohan also be a prince or are sons of the prince not considered to be one

^apparlenty yes also pan’s child or goten s grandchild would be called lord

^accoridng to the uk anyway and I don’t know the validity of the last statement but I don’t care enough to look it up

That's not how that works. if you marry a princess, you don't become a prince. you have to be the son of a king to be a prince.

Nom