The symbol '666' as a number signifying the the number of the Beast in Revelation 13 does not seem to have a preceding source. It's important to recognise that what's going on with 666, or 616 in some manuscript variations, is a form of Gematria. That is, the practice of assigning number values to letters and words, and seeing significance in them.

Recent arguments tend to identify the number with Nero. If that Latin form of his name is transcribed into Hebrew characters you get 616, while the Greek form of his name transliterated into Hebrew gives 666. However there are some problems with this view, it depends upon choosing "Caesar Nero" as the title, a knowledge of Hebrew, and the ambiguity of transliterating into Hebrew. Other name-identifications are possible.

Alternatively, the number has been interpreted as not a form of gematria, but simply a figurative number based on intra-Biblical symbolism (cf. the use of 7, 12, 24, 144,000, etc..) This interpretation tends to head down the line of 6 in contrast to 7, so incompleteness against wholeness.

tl, dr: 666 probably doesn't have a meaning before Christianity. Unlike other symbols adopted/adapted, it seems like this one is native to early Christian writing. However it's exact meaning is uncertain.

It's from the Book of Revelation, the last book of the Bible, written around CE 95: "Then I saw another beast that rose out of the earth; it had two horns like a lamb and it spoke like a dragon. It exercises all the authority of the first beast on its behalf, and it makes the earth and its inhabitants worship the first beast, whose mortal wound had been healed. It performs great signs, even making fire come down from heaven to earth in the sight of all; and by the signs that it is allowed to perform on behalf of the beast, it deceives the inhabitants of earth, telling them to make an image for the beast that had been wounded by the sword and yet lived; and it was allowed to give breath to the image of the beast so that the image of the beast could even speak and cause those who would not worship the image of the beast to be killed. Also it causes all, both small and great, both rich and poor, both free and slave, to be marked on the right hand or the forehead, so that no one can buy or sell who does not have the mark, that is, the name of the beast or the number of its name. This calls for wisdom: let anyone with understanding calculate the number of the beast, for it is the number of a person. Its number is six hundred sixty-six." -Revelations 13:11-18

There are ancient manuscripts that have the number 616, rather than 666 - unfortunately I do not have my college books to quote them (they are in my parents' house) but here is a 2005 news article about one of these manuscripts.

The prevailing academic theory is that the number is a kind of code for the name of some important man of the time whom the author considered a threat to early Christianity. The professor quoted in the article again claims it refers to Caligula, but Nero is more commonly floated as a possibility. Here is a video demonstrating how the code worked.