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"The Big Cube" of the title is slang for a sugar cube dipped in LSD, which is omnipresent throughout the movie. Adriana Roman (Lana Turner) is a famous actress who is retiring from the stage to marry wealthy Charles Winthrop (Dan O'Herlihy), a situation that displeases Winthrop's daughter Lisa. While hanging out at a nightclub called "Le Trip,"Lisa is shown the bizarre effects that LSD-laced sugar cubes can have when added to a drink. She also meets Johnny Allen, a drug dealer who, once he learns that Lisa comes from money, is anxious to marry her. While Adriana and Winthrop are away, Lisa and Johnny hold a wild drug and sex party at her home. When her father walks in on it, he forbids Lisa's marriage. Soon thereafter, Winthrop drowns at sea, but Adriana follows his orders that Lisa will be disinherited if she marries Johnny. The two plot their revenge by lacing Adriana's sleeping pills with LSD, to the point that she goes mad and is committed to an asylum. Lisa and Johnny marry, but when Johnny takes Lisa's best friend to bed, Lisa regrets her actions. She tells Frederick Lansdale, a playwright friend of her stepmother's, what she has done. He has the notion of writing a play based on Adriana's experiences, and convincing Adriana to play the lead role. Amazingly, going through this experience cures Adriana – just as Lansdale hoped it would.