The Bible is consistent with archaeology:
Not Cyrus the Great but his grandson Xerxes, intro:
In the the books of Daniel + Ezra Koresh uses the title initiated by Xerxes. Furthermore in the book of Daniel king Darius still uses the title in use until Darius I (king of the Chaldeans = Babylonians). Therefore you find this turning point of the king's title within the book of Daniel, identifying both kings mentioned there.
It is strange however in the books Daniel and Esther the kings reign over an empire 100 areas greater than what is known from archaeological finds, namely 120 and 127 against 20 and 27 (Daniel 6:29, Esther 1:1). Gesenius' lexicon explains this however: the word 100 also can be translated as tax. Thus Daniel 6:29 states how Darius I organized his empire: with 20 tax owing satrapies.
The Elephantine papyri mention the high priest of Ezra also was high priest during the last years of the reign of Darius II, identifying the Darius of the book of Ezra.
Persian kings in the book of Daniel:
The king's title changed with Xerxes as noted by Roman Ghirshman in his book Iran (page 191) from "king of the Babylonians/Chaldeans" to "king of the Persians and the Medes" (2), which change also is visible in the book of Daniel.
This identifies the Persian kings in the book of Daniel as follows:
Darius = Darius I
Darius I did not build in Babylon or the old Persian capital Pasargadae (the centers of power of Cyrus the Great), he did build however in the old Median capital Ecbatana.(3)
The 120 satraps in Daniel 6:2 also can be translated as 20 tribute owing satraps (alternatively 100 means tax) (4) (similar to how Darius I divided his kingdom).
The "about 62 years" mentioned in Daniel 6:1 instead of Darius' age refer to the distance to the destruction of the Jerusalem Temple (a point of reference also used on Jewish grave stones (5) and similar to the distance at Darius I's first year).
Koresh = Xerxes (the grandson of Cyrus the Great and probably his namesake)
The later editor of the book of Daniel considered Daniel the prophet (Daniel 1-5) and Daniel the ruler (Daniel 6) the same person.
However Daniel 6:29 as well as the above identifications indicate they were two distinct individuals living after each-other.
Persian kings in the book of Ezra:
The Elyphantine papyri mention the high priest Johanan, also mentioned in the book of Ezra, as a contemporary of Darius II.(1)
Thus making it possible to identify the kings in the book of Ezra as follows:
Koresh = Xerxes.
Ahasuerus, the Hebrew version of Artachshashta (Aramaic) in Ezra 4 and Nehemiah = Artaxerxes I
Darius in Ezra = Darius II
Confirmed by Ezra 9:9 which notes when Ezra arrived the walls Nehemiah built already were there:
Artachshashta in the book of Ezra during Ezra's appearance = Artaxerxes II
Persian king in the book of Esther:
The ancient historian Herodotus notes in his "Histories" that Xerxes' first wife Amestris also in the later years remained his first wife. She was the daughter of one of Darius I's fellows in arms with whom he conquered the empire. This rules out Xerxes as the king Ahasuerus of the book of Esther.
The only kings ruling from India to Ethiopia as mentioned in the book of Esther following Xerxes are Artaxerxes I and III.
The following appears to identify the king Ahasuerus in the book of Esther as Artaxerxes I:
Originally Artaxerxes I halted the building of the Jerusalem Temple (Ezra 4:21). But later on Nehemiah got a major position within his court. Furthermore his queen influenced him to order resuming the building of the Jerusalem Temple (Nehemiah 2:6).
An uninterrupted chain of Persian kings:
Darius I = Darius in Daniel 6:1
Xerxes = Koresh in Daniel 6:29 + Ezra 1:1 (Xerxes' first year actually is 480 BC instead of 486 BC since the BC dating is about 6 years early)
Artaxerxes I = Ahasuerus (Hebrew) in Ezra 4:6, Artaxerxes a translation of Artachsasta (Aramaic) in Ezra 4:7 - 23 and Nehemia 2:1 - 13:6 and Ahasuerus in Esther 1:1
Darius II = Darius in Ezra 4:24
Artaxerxes II = Artaxerxes a translation of Artachsasta in Ezra 6:14 - 8.1
The duration of the Babylonian exile:
From the first exiles (including Daniel) -> the first year of Xerxes = 120 years
From the destruction of the Jerusalem Temple -> the first year of Xerxes = 100 years
The above indicates Jesus was born 480 years after the return to Israel (1 Kings 6:1, Ezra 3:1-4, John 2:19-21).
(1) James B. Pritchard, Ancient Near Eastern Texts Relating to the Old Testament, Princeton University Press, third edition with supplement (1969), p. 492.
(1) Bezalel Porten (Author), J. J. Farber (Author), C. J. F. Martin (Author), G. Vittmann (Author), The Elephantine Papyri in English (Documenta Et Monumenta Orientis Antiqui, book 22), Koninklijke Brill NV, The Netherlands, 1996, p 125-153.
(2) Roman Ghirshman, Iran (1954), Penguin Books, p 191.
(3) Karl Julius Ploetz, A Handbook of Universal History from the Dawn of Civilization to the Outbreak of the Great War of 1914.
(4) Wilhelm Gesenius, Hebräisches und Aramäisches Handwörterbuch über das Alte Testament, 17. Auflage (1962), Springer-Verlag, p 392.