I'm interested in this question because some liberal theologians insist that the Bible does not say anything about premarital sex*. To get a reasonable scope for the question, I limit this to just the 5 instances in 1 Corinthians, out of in total 26 instances of πορνεία in the New Testament.
These four verses seem like they could indeed mean premarital sex; however, I don't have any proof that would withstand scrutiny.
1 Corinthians 5:1 (KJV)
It is reported commonly that there is fornication among you, and such fornication as is not so much as named among the Gentiles, that one should have his father's wife.
1 Corinthians 6:13 (KJV)
Meats for the belly, and the belly for meats: but God shall destroy both it and them. Now the body is not for fornication, but for the Lord; and the Lord for the body.
1 Corinthians 6:18 (KJV)
Flee fornication. Every sin that a man doeth is without the body; but he that committeth fornication sinneth against his own body.
1 Corinthians 7:2 (KJV)
Nevertheless, to avoid fornication, let every man have his own wife, and let every woman have her own husband.
The King James Bible translates these as fornication (as it also does πορνεύω in 6:18, which is a different word). Don't get tangled up with the meaning of fornication; the question is about the original Greek word.
So, what does Paul mean with his use of πορνεία in these passages? Quite obviously it's some sort of sexual immorality, but does the intended meaning include premarital sex? Or is it reasonable to claim that it only means other kinds of sexual immorality?
*Which I think it does, let that be known. I'm not the one trying to justify premarital sex. I want to find a well-grounded argument against these claims.
The question is a refocused version of my earlier question on Christianity.SE: Is premarital sex πορνεία (porneia)? That question also includes links to two academic papers (1, 2) that might be relevant if someone can get hold of them and understand the arguments they make.