In the Cyrus Cylinder, Cyrus talks about the god of Babylon, Marduk, as being the one who has given him authority. But this should not cause us to doubt the Bible text. Cyrus probably told all the people groups whom he let go that their god was the one who had told him to do so.
2 “Thus says Cyrus king of Persia: The LORD, the God of heaven, has given me all the kingdoms of the earth, and he has charged me to build him a house at Jerusalem, which is in Judah.