Which king's reign began in 586 BC and ended in 516 BC during the Babylonian Captivity?

The reign that is noted to have begun in 586 BC and ended in 516 BC during the Babylonian Captivity is linked to Cyrus. He was the king of Persia who played a pivotal role in the return of the exiled Jewish population to their homeland after the Babylonian captivity.

Cyrus's decree in 538 BC allowed the Jews to return to Jerusalem and rebuild the temple, marking a significant moment in Jewish history and fulfilling prophesies regarding their return. His reign is essential to understanding the end of the Babylonian Captivity, as it transitioned the Jewish experience from exile under Babylonian rule to restoration under Persian rule.

Darius also played a role during this period, particularly in the completion of the temple in Jerusalem after Cyrus's initial decree, but his reign does not align with the specific dates given in the question. Josiah and Zedekiah were kings who reigned prior to this captivity, making them unrelated to the specific timeline noted.