"And these shall go away into everlasting punishment: but the righteous into life eternal."
It is well to notice that Jesus did not say that the wicked would suffer "everlasting punishing." He said "everlasting punishment." What is the punishment for sin? "Them that know not God... shall be punished with everlasting destruction from the presence of the Lord." 2 Thessalonians 1:9. There it is--plainly spelled out. The punishment is destruction, and it is of eternal duration. In other words, it is a destruction which never ends because there will be no resurrection from that destruction.
Paul says, "The wages of sin is death." Romans 6:23. John describes that death as "the second death" in Revelation 21:8. That death, or destruction, will be eternal--Answers to Difficult Bible Texts.