kepler:
Despite a number of references to Ezra, I don't think there was any mention of this Ez 6:15-18:
The Temple was completed on the 23rd day of the month of Adar in the sixth year of the reigh of King Darius. The Israelites - the priests, the Levites and the remainder of the exiles - joyfully celebrated the dedication of the Temple of God - for the dedication of this Temple of God they offered one hundred bulls, two hundred rams, four hundred lambs... They installed the priests in their orders and the Livites in their positions for the ministry of the Temple of God in Jerusalem, as prescribed in the Book of Moses.
In other words, the Temple was not complete until it was dedicated on a specific date.
What was the date? That was about 1 April 515 BC according to a footnote in my Bible. Elsewhere I have seen it described as 516. E.g., Wikipedia.
Now what was going on 70 years earlier?
Elsewhere Jews have interpreted this 70 year desolation accordingly.
That may seem convenient, but completion of the temple hardly bares any resemblance to 'all the nations serving Babylon'. And the temple's completion in early 515 BCE (it was completed in their twelfth month,prior to Nisan, and so it was the year that started in our 516 BCE per some sources) is more than 70 years after mid 587 BCE anyway.
However, you may be alluding to the other 70 years - the 70 years of fasting mentioned in Zechariah. That period runs from 587 BCE until Darius' fourth year, 518 BCE (after the fasts had been held in that 70th year).
Strangely enough, if we take the present era dating and the second temple's destruction, we get another 70 year interval.
That's what we call a coincidence. Usage of AD wasn't introduced until the sixth century. (CE became widely used in the 20th century but has been used since at least the 19th century.) The start of the 'era' is based on a supposed date for the birth of Jesus that is wrong even if Jesus actually existed. The correlation you're making is therefore entirely arbitrary.