Who was the king of Cheshbon, mentioned in Bamidbar?
Perhaps you mean the king of Cheshbon?
Cheshbon was the capital city of Sichon, king of the Amorites ("Emorim"). The Jews conquered it.
See Numbers 21:21--27:
Israel sent emissaries to Sichon king of the Amorites ... Sichon, however, did not let Israel pass through his territories. Instead, Sichon mustered up all his people, and went out to confront Israel in the desert. When he came to Yahatz, he attacked Israel. ... Israel thus took all these cities. They [later] settled in Cheshbon and all its tributary towns, all the Amorite cities. ... Cheshbon was the capital of Sichon king of the Amorites. ... The minstrels therefore say: Come to Cheshbon! Let Sichon's city be built and established!
The verses indicate that the Amorites conquered land from the Moabites; some commentaries read these verses as saying that Cheshbon had always been Amorite ("let Sichon's city be built and established!"); others read it that Cheshbon was also part of the conquest ("let it become established as Sichon's city").