From my new book, The  Atonement:  A  Biblical,  Theological,  and  Historical  Study  of  the  Cross  of  Christ (Nashville: B&H Academic, 2019):

The atonement of Christ is inextricably linked with His resurrection (1 Cor 15:3–4). Crucifixion cannot be separated from and given priority over resurrection. Both the cross and the resurrection are the central themes of apostolic preaching. If Christ has not risen from the dead, we are still in our sins, according to 1 Corinthians 15. Both the cross and the resurrection are events necessary for the salvation of humanity (Mark 8:31). In the resurrection we have God’s great “Not Guilty!” overturning humanity’s verdict “Crucify Him!”

As H. D. McDonald states,

“It is in the resurrection that the saving actuality of the cross is realizable.  The resurrection is the affirmation of the atonement. It is the divine guarantee that our sins, with their guilt and penalty, have been dealt with. . . . By means of the cross and empty tomb the salvation of God has become historical and eternal. Christ’s atonement is historically absolute in the cross and eternally actual in the resurrection. . . .Without the cross the resurrection might have been seen as a miracle but with no relation to men’s lives, and without the resurrection the cross must have been seen as a mistake with no relation to their sin. Without the resurrection the cross cannot be understood as atoning, and without the cross the resurrection cannot be experienced as redeeming” (H. D. McDonald, The Atonement of the Death of Christ, 38–40).

I love the way the great James Denney put it: “There can be no salvation from sin unless there is a living Saviour: this explains the emphasis laid by the apostle on the resurrection. But the Living One can only be a Saviour because he has died: this explains the emphasis laid on the Cross” (Denney, The Death of Christ, 123).