Tacitus writing in the Annals in about 116 A.D.:
"Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilatus, and a most mischievous superstition, thus checked for the moment, again broke out not only in Judæa, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their centre and become popular."
Pliny the Younger in a letter to the Emperor Trajan in about 112 A.D. asking how to proceed with the Christians:
They were in the habit of meeting on a certain fixed day before it was light, when they sang in alternate verses a hymn to Christ, as to a god, and bound themselves by a solemn oath, not to any wicked deeds, but never to commit any fraud, theft or adultery, never to falsify their word, nor deny a trust when they should be called upon to deliver it up; after which it was their custom to separate, and then reassemble to partake of food--but food of an ordinary and innocent kind.
And now Caesar, upon hearing the death of Festus, sent Albinus into Judea, as procurator. But the king deprived Joseph of the high priesthood, and bestowed the succession to that dignity on the son of Ananus, who was also himself called Ananus... Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrin of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned.
and
Now some of the Jews thought that the destruction of Herod's army came from God, and that very justly, as a punishment of what he did against John, that was called the Baptist: for Herod slew him, who was a good man... Herod, who feared lest the great influence John had over the people might put it into his power and inclination to raise a rebellion... Accordingly he was sent a prisoner, out of Herod's suspicious temper, to Macherus, the castle I before mentioned, and was there put to death.
Those extra-biblical references don’t cause me any trouble at all. As I said, he probably DID exist and have followers. There are always charismatic men with followers about. David Koresh had followers. Stalin had followers.