There is an infinite number of things which happened in the past which are not known to historians. In the case of Darius the Mede, there is one very good historical source. In fact there is a record of his rule of the province of Babylon in the time immediately after the conquest by Cyrus in what is certainly the most reliable historical source we have from the ancient Near East: The Old Testament. By the way, we cannot list all the rulers of the province of Babylon after the conquest of Cyrus with the exact years they ruled. We do know about Gubaru. Some have proposed that Gubaru is actually another name for Darius, as he was a Mede, but this is a bit speculative. Absence of evidence (outside the book of Daniel) is not evidence of absence, unless we have a complete and uninterrupted list of the rulers of the province of Babylon from the time of Cyrus.
It is very instrucive to remember that skeptics of Daniel were unanimous in declaring the existence of king Belshazzar in Daniel 5 a mistake until they found reference to him ruling as regent under Nabonidus in an inscription at the Ziggurat in Ur. This explains why Belshazzar offered Daniel the third (not the second) place in his kingdom if he could interpret the writing on the wall. This example should make us cautious about labeling a character in Daniel as fictitious simply because we do not have an extant source on that character. Before this inscription we had all the rulers of Babylon, leaving no room for Belshazzar. Clearly, Belshazzar was a far more significant player in the world scene that Darius the Mede, yet we knew nothing of him (except in the most reliable historical source we have: the Bible!) until quite recently. I will admit that my analogy in the case of Belshazzar does not prove that Darius ruled Babylon. Analogy is not proof, but it certainly illustrates why lack of evidence is not evidence of lack.
Why the Cambridge History of Judaism does not list Darius the Mede is something they will have to answer for themselves. I am going to guess that this comes from liberal theologians who do not accept that the Bible is inspired by God. It is fashionable to ignore our most reliable historical source from the period out of a religiously-inspired bias against the Old Testament. No one doubts Herodotus, and even Josephus is accepted over the Old Testament, even though he wrote hundreds of years after the OT writers. Such bias and prejudice explains a lot.
John Oakes, PhD