"Wherefore it is said in the book of the Wars of the LORD: Vaheb in Suphah, and the valleys of Arnon, Number 21:14" Dear Rabbai! what is this book?

The Ibn Ezra explains that there used to be such a book but it was lost over time, and the Ramban (v. 13) points out that this was an ancient custom, for nations to write such events (as archeologists in fact found). It was not holy nor part of the Tanach, but it was obviously known at the time the Torah was given. The Talmud in Gittin 38a, explains the importance of this as a "legal explanation" or proof, for we are taught not to fight nor conquer Amon and Moav (Devarim 2, 9) for their land was given to them as the children of Lot, but after Sichon and Og conquered it from them, we are then allowed to conquer it from the conquerers, for they have nothing to do with Lot.