What is for the sake of Yakov?
Rashi: I will take them out of Galus Bavel.
Radak: I give to [Koresh] strength, to destroy Bavel. It is not for him, rather, for Yisrael (to take them out of Galus Bavel), for Bavel subjugated them too harshly.
Why does it say "Yakov v'Yisrael Bechiri"?
Malbim: Even though their Avodah is at a low level (Yakov) - they were not absolute Tzadikim at the time - they are "Yisrael Bechiri." I chose them for My portion. They are called Yisrael - a high level and grandeur. The miracles that Hashem does for His 'needs' are not prophesized beforehand. What He does for Yisrael, Nevi'im tell them beforehand.
Why does it say "va'Ekra Lecha bi'Shmecha" and "Achancha"?
Radak: Sometimes the verse calls Koresh by his name, and sometimes he is not mentioned (only a pronoun).
Malbim: Since I do for Yisrael, I gave Nevu'os about this, and called you with the name of honor.
Why does it say "v'Lo Yedatani"?
Rashi: You did not do My desire. I said that he should build My city, but he said 'who will go up among you
