Notice the context of the scripture that nearly everyone uses to define the gospel. 1 Corinthians 15:
1Now I would remind you, brothers,a of the gospel I preached to you, which you received, in which you stand, 2and by which you are being saved, if you hold fast to the word I preached to you—unless you believed in vain.
3For I delivered to you as of first importance what I also received: that Christ died for our sins in accordance with the Scriptures, 4that he was buried, that he was raised on the third day in accordance with the Scriptures, 5and that he appeared to Cephas, then to the twelve.6Then he appeared to more than five hundred brothers at one time, most of whom are still alive, though some have fallen asleep. 7Then he appeared to James, then to all the apostles. 8Last of all, as to one untimely born, he appeared also to me. 11Whether then it was I or they, so we preach and so you believed. 15 We testified about God that he raised Christ
In the same chapter about the gospel:
And if Christ has not been raised, then our preaching is in vain and your faith is in vain. We are even found to be misrepresenting God, because we testified about God that he raised Christ, whom he did not raise if it is true that the dead are not raised. For if the dead are not raised, not even Christ has been raised. And if Christ has not been raised, your faith is futile and you are still in your sins. Then those also who have fallen asleep in Christ have perished. If in Christ we have hope in this life only, we are of all people most to be pitied. But in fact Christ has been raised from the dead, the firstfruits of those who have fallen asleep. For as by a man came death, by a man has come also the resurrection of the dead. (1 Corinthians 15:14-21)
So is it with the resurrection of the dead. What is sown is perishable; what is raised is imperishable. It is sown in dishonor; it is raised in glory. It is sown in weakness; it is raised in power. (1 Corinthians 15:42-43)
Peter's famous speech in Acts chapter 2:
23this Jesus, delivered up according to the definite plan and foreknowledge of God, you crucified and killed by the hands of lawless men. 24God raised him up, loosing the pangs of death, because it was not possible for him to be held by it.
29“Brothers, I may say to you with confidence about the patriarch David that he both died and was buried, and his tomb is with us to this day. 30Being therefore a prophet, and knowing that God had sworn with an oath to him that he would set one of his descendants on his throne, 31he foresaw and spoke about the resurrection of the Christ, that he was not abandoned to Hades, nor did his flesh see corruption. 32This Jesus God raised up, and of that we all are witnesses.
Peter's message to Cornelius, the "words by which you will be saved" included the resurrection:
And we are witnesses of all that he did both in the country of the Jews and in Jerusalem. They put him to death by hanging him on a tree, but God raised him on the third day and made him to appear, not to all the people but to us who had been chosen by God as witnesses, who ate and drank with him after he rose from the dead. (Acts 11:14; 10:34-43)
I hope this has helped us all see that the resurrection is an essential part of the gospel. The resurrection frees us from death and sin.
He was delivered over to death for our sins and was raised to life for our justification (Romans 4:25)
That if you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved; for with the heart a person believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation. (Romans 10: 9-10)
“Death is swallowed up in victory.”
“O death, where is your victory?O death, where is your sting?” (1 Corinthians 15:55)