There have been several sources that have been said to be non-biblical references to Jesus: Josephus, Tacitus, and Suetonius being the most popular. The obvious problem with these three authors is that neither lived during the time of Jesus. Josephus lived c. 37 - 100 CE; Tacitus c. 55 - 117 CE; Suetonius c. 69 - 140 CE.
For the undereducated among us, "c." refers to "circa" or "about" and "CE" refers to "Common Era," also known as "AD."
The most popular of these so-called non-biblical confirmations of Jesus was written by Josephus. But there are a lot of problems with his work. First, there's the time differential: The alleged Christ died before Josephus was born. Second, Josephus was an Orthodox Jew, yet he is supposed to have written of one who was to be the answer to his messianic hopes?
Third, if Jesus was so important to Josephus -a messiah- why only devote a paragraph? Indeed, the entire passage of about 127 words appears out of place and inserted. Josephus refers to the story of Jesus as a "terrible misfortune," hardly the position expected of an Orthodox Jew. The expected opinion of a Christian, but not a Jew! It seems clear that early Christians went about redacting and editing many historical documents in their attempts to justify their cult and gain some ground over other, more established, cults like the Judaic.