Why does the Torah need to mention that Sichon captured land from the first king of Mo'av?
Rashi and Ramban: Because otherwise, Yisrael, who were commanded not to attack Mo'av, 1 would not have been permitted to capture those areas. 2
Oznayim la'Torah: In light of what the Torah writes "u'Balak ... Melech le'Mo'av ba'Eis ha'Hi" (22:4), it is telling us here that the battle between Sichon and Mo'av took place in the time of the first king of Mo'av who preceded Balak, the current king.
Rashi: See Devarim, 2:9.
Rashi (citing Chulin, 60b): 'Amon and Mo'av became permitted to Yisrael via Sichon'. See also Torah Temimah, note 22, who elaborates.
Why does the Torah need to inform us that Cheshbon was the city of Sichon?
Da'as Zekenim and Hadar Zekenim: So that one should not say that it belongs to Mo'av, in which case Yisrael would be forbidden to take it; only now that Sichon took it from the first king of Mo'av, it now became permitted to Yisrael. 1
Moshav Zekenim: Some say that it was the first city that Sichon conquered from Mo'av; others, that it was initially Sichon's, and he gave it to Mo'av, who had to pay him taxes. However, they rebelled and he cpatured Mo'av's land, including Cheshbon.
