“At that time the work on the house of God in Jerusalem stopped. It was discontinued until the second year of the reign of King Darius of Persia.”
Now we have a problem. There was nothing about stopping the building of the Temple in these 2 letters. It was about the fortifications of the city. On top of that we are back at King Darius who preceded King Artaxerxes by 20 years. Is this a reference to King Darius II, who followed King Artaxerxes? Here are the dates for the ruling kings of Persia. This would put the building of the temple around 423 BCE not 521 BCE. The Persian kings ruled from the following years.
Cyrus the Great – 559-530 BCE – letter to go back to build Temple
Cambyses – 530-522 BCE – no comments
Darius I – 522 -486 BCE – complaints to him
Xerxes I – 485-465 BCE – complaints to him
Artaxerxes I – 465-424 BCE – letter saying to stop wall building
Darius II – 424-400 BCE – rebuilding Temple