There are no contemporary sources that mention Jesus of Nazareth. There are two non-Biblical near-contemporary sources that mention him in passing. One is Antiquities of the Jews, written by Jewish historian Josephus ca 90 AD, which is a history of the Jewish people drawing heavily on the Torah as a source. He mentions Jesus in two passages and John the Baptist in one. None of those passages state much about him other than that he existed and was known as "the Christ" (Greek christos, "the anointed one"). The name "Yeshua" (Greek version "Jesus") was very common in first century Palestine, so it could be any Yeshua, but the appellation of christos makes it pretty certain that it was the same Yeshua that the Gospels are about. The only other source is dated even later, Tacitus, a Roman historian writing ca. 110 AD, and mentions Jesus' execution by order of Pontius Pilate.

The difficulty here is knowing whether either writer was influenced by the Jesus movement and what they "knew" about the life of Jesus based on their gospels. In other words, were Tacitus and Josephus independent sources on the life of Jesus, or did they get their knowledge from the same sources as the writers of the Gospels? Since we still don't even have a clear picture of what the Gospel sources were and how the Gospels relate to each other (which was written first, which writers had already read other Gospels, whether some of the Evangelists were working from the same source documents, etc.) There is and has been an enormous debate among scholars and academics on these questions, and barring another lucky discovery of well-preserved ancient documents, there really is no way to "prove" in a scientific sense what Josephus or Tacitus or the Evangelists "knew" independent of each other, and how they knew it.