Adriana Roman (Lana Turner), a successful stage actress, retires to marry Charles Winthrop (Daniel O'Herlihy), a wealthy tycoon. Winthrop's daughter, Lisa (Karin Mossberg), is instantly distrustful of Adriana solely because she is "the other woman" taking her father's affection.
Charles is killed in a boating accident, which also leads to Adriana suffering from a concussion. Lisa's new boyfriend Johnny Allen (George Chakiris), a womanizing, fortune-hunting medical student, capitalizes on that distrust to persuade Lisa that her father's death was murder, a charge exacerbated by Adriana's threat—as per her late husband's instructions as laid out in his will, for which Adriana is executor—to disinherit Lisa if she marries Johnny.
Johnny conspires with Lisa to lace Adriana's prescribed sedatives with enough LSD to drive her insane. In addition, while Adriana is having LSD-induced hallucinations, they plan on playing pre-recorded subliminal messages to further drive her crazy.
Johnny intends to kill Adriana by adding a recorded message to open the window and jump. Lisa is unaware of his scheme. As Adriana is about to jump to her probable death, Lisa saves her. While still unaware of Johnny's true intent, Lisa continues with their plan and Adriana is committed to a mental hospital, where they have Adriana declared legally insane and thus unable to carry out her obligations in Charles' will.
After their wedding, Johnny demonstrates that he doesn't really love Lisa by openly seducing other women, most notably Lisa's free-spirited best friend, Bibi (Pamela Rodgers). Johnny bribes Lisa to divorce him by providing a $100,000 settlement in return for keeping silent about what they did to Adriana. Lisa does divorce him, but instead of succumbing to Johnny's threats, she decides to come clean to Frederick Lansdale (Richard Egan), a playwright friend of Adriana's who has always loved her himself, about what she and Johnny did. By this time, Adriana was suffering from amnesia, still believing that Charles was alive.
Frederick decides to write a play detailing Adriana's traumatic experiences and casts her in the lead role. He hopes that replaying her experience on stage will cure her. By the opening performance, Adriana has glimpses from her memory of what has happened, not fully realizing what those fleeting thoughts are.
By the climactic third act of the play, which details the taped recorded subliminal messages Lisa and Johnny played during Adriana's hallucinations, Frederick decides to play the actual recordings with Lisa and Johnny's voices. This brings Adriana back to reality. She recognizes the voices and the fact that Lisa and Johnny use her real name as opposed to her character's name in the play. Lisa rushes onto the stage, admitting to Adriana what she and Johnny did. In a rage, Adriana slaps Lisa in the face.
The play and Adriana's performance are a huge hit, Adriana and Frederick are about to be married, and Lisa has reconciled with Adriana. Meanwhile, Johnny has begun taking his own LSD while being shunned by his so-called friends. He is last seen on the floor in the midst of an LSD trip.
The Big Cube was released in 2007 as part of Volume 2 of Warner Brothers' Cult Camp Classic's "Women in Peril" series, a three-part series that included John Cromwell's Caged and the film that gave Joan Crawford her last starring role, Freddie Francis' Trog.