What poem has a similar theme to "The Cask of Amontillado?"The poem has to be written by Poe.
The tow most prevalent themes in Edgar Allan Poe's short story "The Cask of Amontillado" are revenge and atonement/forgiveness. While many of Poe's short stories contained themes similar to these, it can be rather difficult to find a poem which shares either of the themes as well.
That being said, if one were to add the theme of solitude, alienation, or mystery one could easily find a poem which matches the theme. Based upon this, one could use Poe's poem "Spirits of the Dead" to mirror the themes from "The Cask of Amontillado."
The poem speaks to the fact that once one is dead, no one will be able to hear them or help them. The dead are forced to be silent, much like Fortunato. The poem also mentions illness, again similar to the sickly Fortunato,"To thy weariness shall seem / As a burning and a fever."
In the end, the poem speaks to the mysteries associated with the dead. This could mirror the short story based upon the fact that Fortunato's disappearance will be a mystery to those who know him and will miss him.