To my knowledge, and correct me if I am wrong, the Bible does not mention specifically pre-marital sex. It does say lots of things about fornicators, sexual immorality, so if for you, all pre-marital sex falls under fornication and sexual immorality, there you have it:
"Do you not know that the wicked will not inherit the kingdom of God? Do not be deceived: Neither the sexually immoral nor idolaters nor adulterers nor male prostitutes nor homosexual offenders nor thieves nor the greedy nor drunkards nor slanderers nor swindlers will inherit the kingdom of God." (1 Corinthians 6:9-10)
"We should not commit sexual immorality, as some of them did--and in one day twenty-three thousand of them died." (1 Corinthians 10:8)
"Marriage should be honored by all, and the marriage bed kept pure, for God will judge the adulterer and all the sexually immoral." (Hebrews 13:4)
Edited to add:
"Now to the unmarried and the widows I say: It is good for them to stay unmarried, as I am. But if they cannot control themselves, they should marry, for it is better to marry than to burn with passion." (1 Corinthians 7:8-9)
"Now concerning the things whereof ye wrote unto me: It is good for a man not to touch a woman. Nevertheless, to avoid fornication, let every man have his own wife, and let every woman have her own husband." (1 Corinthians 7:1-2, KJV)
The word fornication comes from the latin word fornix (from which fornicti, the ancestor of fornication, is derived) which meant "a vault, an arch." The term also referred to a vaulted cellar or similar place where prostitutes plied their trade. Fornication is the word which many Bible scholars use for translating the Greek word porneia into English. The word porneia itself can mean adultery, incest, prostitution, idolatry. So, the word fornication and its Greek equivalent were pretty broad and most likely, given the historical contexts, covered also sexual relationships outside of marriage.
