In 'Cube Conundrum: The Quantum Heist', players assume the role of a quirky but brilliant mathematician who has stumbled upon a secret organization that manipulates time and space using a mysterious flat cube. Tasked with infiltrating this organization, players must solve complex mathematical puzzles and navigate through richly described environments filled with historical figures, futuristic tech, and alternate dimensions. The narrative unfolds based on the choices players make and the puzzles they solve, leading to multiple endings where the fate of time itself hangs in the balance.