Like many Poe stories, "The Black Cat" and "The Cask of Amontillado" share many commonalities. Below are just a few.
1. Both possess unreliable narrators, a common Poe element. "The Black Cat's" narrator admits that he is under the influence of alcohol and possibly even insanity. He once loved animals but then begins to torture them for no apparent reason. Similarly, "The Cask of Amontillado" features a narrator, Montresor, who seeks revenge upon Fortunato who does not even seem to know that he has done anything wrong. Montresor is sane enough to plot out an intricate murder; yet he does not even specifically mention Fortunato's "sin" or explain to Fortunato before his death why he is being killed.
2. Both stories involve live burials in which creatures/humans are bricked up behind a wall. In "Cat," the narrator tries to hide his wife's body behind a brick wall that he creates after accidentally killing her, but he also ends up trapping the cat behind the wall. In "Cask," Montresor knowingly "buries" Fortunato behind a brick wall while he is still alive.
3. Both stories to involve murder. While the narrator in "Cat" does not set out to kill his wife, he certainly shows no regret after he buries an axe in her brain, and Montresor plot his murder of Fortunato for weeks.
4. Both stories involve somewhat of an obsession with alcohol. The narrator of "Cat" states that his disease is alcohol and that that is what causes him to abuse animals in the first place. Likewise, besides the title of "Cask," obsession with unique wines leads him to let down his guard with Montresor who uses Fortunato's wine interest to kill him.