CalebInFloroda: To begin with, when the First Temple fell, according to Jewish history and tradition, Nebuchadnezzar took the House of David and cared for it in a special place where the descendants of the monarchy could still retain some freedom as well as the dignity afforded royalty. According to tradition and Scripture, the Babylonians had control of the Iberian Peninsula, which is Sepharad or modern Spain and Portugal.
There does not seem to be any secular reference to Nebuchnezzar's political or military authority reaching as far as modern day Spain.
The web-site Livius, which may be regarded as speaking with some authority, certainly does not mention it, not, at least, in my rather hurried scanning.
Link: http://www.livius.org/articles/place/babylonian-empire/
I think the confusion has arisen, somewhere, somehow, between the Iberian peninsula and the Kingdom of Iberia located in Asia, near Georgia.
Wikipedia is not the best reference in the circumstances, but I choose it because it has a reasonable map.
Link: https://en.wikipedia.org/wiki/Kingdom_of_Iberia
As you can note, both the location and the dates of this Asian Iberia fit the historical details.
BTW, If we are seeing the bible as a historical record, it is quite specific as to the numbers of people deported to Babylon, actually not a very large group of people in total and clearly comprising the elite, who ( from their own viewpoint) comprised the 'nation'. The common people were not deported and the land was never left physically desolate, although in the view of the elite, it may have been spiritually desolate.
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2. This is not an argument that there were no Jews in what we now call Spain. There are many references to Jewish migrants in many locations in both the Hellenic and Roman empires. The Jews who refused to return to Jerusalem and stayed behind in Babylon became famous as traders, with groups of Jews in all the major trade markets of the east-west trade network (the silk road). One collection, known as the Radhanites (although that may have been a tag that referred to all) were particularly active in the Euro-Asian slave trade and are reputed to have maintained a facility in Verdun for castrating boys for the eunuch market.
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3. At this link: ( http://ccat.sas.upenn.edu/nets/edition/40-daniel-nets.pdf ) there is a copy of, 'A New English Translation of the Septuagint,' published by Oxford University Press. The Introduction may be of interest to some readers here.