Darius the Mede is distinct from later Persian kings named Darius (see “The Medes and Persians” Profile). Cyrus the Great conquered Babylon in 539 BC, and there is no mention of a Darius the Mede in other sources. Two solutions are possible:
Cyrus the Great might have chosen Darius the Mede to rule as “King of Babylon” in his place for a little over a year (compare Dan 6:28; 9:1; 11:1).
Darius and Cyrus might have been the same man bearing two throne names—one name from the Medes, the other from the Persians (see also study note on 6:28).
The portrayal of Darius in ch 6 suggests that he was in fact Cyrus, the ruler of all Media, Persia, and Babylonia.