26 Therefore, they have drunk out of the cup of the wrath of God, which justice could no more deny unto them than it could deny that Adam should fall because of his partaking of the forbidden fruit; therefore, mercy could have claim on them no more forever.
27 And their torment is as a lake of fire and brimstone, whose flames are unquenchable, and whose smoke ascendeth up forever and ever. Thus hath the Lord commanded me. Amen.
Compare with Psalms 11:6
6 Upon the wicked he shall rain snares, fire and brimstone, and an horrible tempest: this shall be the portion of their cup.
7 For the righteous Lord loveth righteousness; his countenance doth behold the upright.
Note that "righteous" in Psalms 11:7 is the Hebrew adjective, tsaddiq, which also means "just".
King Benjamin uses the same symbolism in the previous chapter too:
33 For behold, there is a wo pronounced upon him who listeth to obey that spirit; for if he listeth to obey him, and remaineth and dieth in his sins, the same drinketh damnation to his own soul...
38 Therefore if that man repenteth not, and remaineth and dieth an enemy to God, the demands of divine justice do awaken his immortal soul to a lively sense of his own guilt, which doth cause him to shrink from the presence of the Lord, and doth fill his breast with guilt, and pain, and anguish, which is like an unquenchable fire, whose flame ascendeth up forever and ever.
Only the Psalmist connects the cup imagery with fire and brimstone like King Benjamin. But generally, this symbolism of a cup or drinking is found several times in the Bible. For instance, in Isaiah 51:17
Awake, awake, stand up, O Jerusalem, which hast drunk at the hand of the Lord the cup of his fury; thou hast drunken the dregs of the cup of trembling, and wrung them out.
Similar language is found in Jeremiah, Zechariah, Revelations among others. The most famous is perhaps Jesus in Gethsemane
And he went a little further, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt. (Matthew 26:39)
The "divine justice" that King Benjamin talked about necessitated the drinking of that cup. It was as inevitable as Adam's fall "because of his partaking of the forbidden fruit". The message is simple: If we repent, mercy is in effect and Christ will drink the cup. If we don't repent, justice is in effect and we must drink the cup.
16 For behold, I, God, have suffered these things for all, that they might not suffer if they would repent;
17 But if they would not repent they must suffer even as I;
18 Which suffering caused myself, even God, the greatest of all, to tremble because of pain, and to bleed at every pore, and to suffer both body and spirit—and would that I might not drink the bitter cup, and shrink—
19 Nevertheless, glory be to the Father, and I partook and finished my preparations unto the children of men. (D&C 19)