Actually, the Council of Nicaea didn't alter the Bible at all. We have a record of all the canons from the Council; it set the date of Easter, settled several points of church discipline, and - most prominently - ruled that Jesus is of the same being and substance [homoousion] as God the Father. That was supposed to settle the controversy over the Arian heresy which had threatened to rip the Church apart; unfortunately, the Arians would become even more prominent over the next generation or two until the First Council of Constantinople reaffirmed Nicaea. Here's a previous thread with an in-depth look at the history leading up to the Council.

In short, the Council of Nicaea had absolutely nothing to do with the text of the Bible, nor with the canon (which was generally settled at that point, but not completely, as you can see from Eusebius's list in his Church History). While there have been some interpolations into individual manuscripts of the Bible, there was never a coordinated effort to change every manuscript's text.