In Daniel 6:30, the king who conquered and took over the Babylonian empire was Darius, while I guess historical records indicate it was Cyrus. What would you say about this? Cyrus is referred to in Daniel 1:21. Was the year Daniel was put into the lions' den before the first year
of the king Cyrus?—Tadashi Tsumura (Osaka)

Yes, Dan 6:30 makes is sound as if Cyrus came after Darius—which is not correct historically. Yet the Bible actually has Cyrus as the first Persian king. He is referred to often in the second half of Isaiah—even by name in Isa 44 and 45. Cyrus was called Shahanshah, or "king of kings." His decree returning the Jews to Jerusalem, and providing imperial funding for the rebuilding of the Jerusalem temple, may be found on an important archaeological discovery called the Cyrus Cylinder. (See photograph below.) You can get the gist also reading the every end of 2 Chronicles, or the beginning of the next chapter, Ezra 1.

In the first year of Cyrus king of Persia, in order to fulfil the word of the Lord spoken by Jeremiah, the Lord moved the heart of Cyrus king of Persia to make a proclamation throughout his realm and also to put it in writing:

“This is what Cyrus king of Persia says:

'The Lord, the God of heaven, has given me all the kingdoms of the earth and he has appointed me to build a temple for him at Jerusalem in Judah. Any of his people among you may go up, and may the Lord their God be with them.'" (2 Chron 36:22-23)

Cyrus’s entry into Babylon is recorded in the Nabidonus Chronicle. Cyrus proclaimed, "When my soldiers in great numbers peacefully entered Babylon... I did not allow anyone to terrorise the people... I kept in view the needs of the people and all their sanctuaries to promote their well-being... I freed all the slaves."