ציטירנדיקער פּירוש אויף עזרא 1:2

There was still another year left for Babylonia: Thus is it found in Seder Olam: "In that night Belshazzar, the king [...], was slain. And Darius the Mede received the kingdom" (Daniel 5:30 - 6:1). Behold that is seventy years from the day that Nebuchadnezzar reigned; sixty-nine from the day that he conquered Yehoyakim; and still one more year 'for Babylonia,' for the completion of the seventy years from when he ruled over Israel - and Darius rose and completed it. And after him, in the next year, Cyrus reigned in Babylonia and they were partially remembered. As he said, "Anyone of you of all His people—may his God be with him, and let him go up, etc." (Ezra 1:2). We learned from this baraita that when Belshazzar died, there were only sixty-nine years from the conquest of Yehoyakim. But above we counted seventy years: Forty-five of Nebuchadnezzar, twenty-three of Evil-merodach and three of Belshazzar. Hence [some of them] were partial years.

The world. Cyrus conquered many countries, as he says; All the kingdoms of the earth the Lord, the God of heavens, hath given me (Ezr. 1:2)

And five of Darius the Mede and Cyrus the Persian: As it is written (Daniel 6:1), "And Darius the Mede received the kingdom." And after him, Cyrus the First reigned. For he gave permission to the exiles to ascend [back to Israel], as it is stated (Ezra 1:2), "Thus said Cyrus, etc." And it would come up in your mind now that, between the two of them, they had reigned for five years - even though it is not written in Scripture.

from the rising of the sun he shall call in My name (Ezra 1:2) “All the kingdoms of the earth has the Lord God of the heavens given me.” And it appears that Persia is northeast of Eretz Israel. Another explanation is: I aroused Nebuchadnezzar from the north to destroy My city, and he came, and I aroused Cyrus from the east, that he call in My name to build My city, for the kingdom of Persia is east of Eretz Israel, as it is stated (Dan. 8:4): “I saw the ram butting etc.” [This verse in Daniel proves it. “I saw the ram butting to the west and to the north and to the south.” We deduce that he came from the east.] Jonathan paraphrases: I brought speedily a king, strong as the north wind, and he will come as the sun comes out with its might from the east; I will strengthen him with My name.

a rumor that is good for you [viz.] “So said Cyrus, the king of Persia..., Whoever among you of all His people...” (Ezra 1:2f).