Absolutely. That is precisely what the Bible says.
The next day John seeth Jesus coming unto him, and saith, Behold the Lamb of God, which taketh away the sin of the world. (Jn 1:29)
I am the living bread which came down from heaven: if any man eat of this bread, he shall live for ever: and the bread that I will give is my flesh, which I will give for the life of the world. (Jn 6:51)
But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honour; that he by the grace of God should taste death for every man. (Heb 2:9)
For there is one God, and one mediator between God and men, the man Christ Jesus; Who gave himself a ransom for all, to be testified in due time. (1 Tim 2:5,6)
My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous: And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world. (1 Jn 2:1,2)
All we like sheep have gone astray; we have turned every one to his own way; and the LORD hath laid on him the iniquity of us all. (Isa 53:6)
The question you should be asking yourself is "When did I stop believing God and chose to believe the lies of men?"
So Christ died for every sin of every man. Ok, so then why do some go to heaven, and others do not?