Other mistake: Toward the beginning, when the characters wonder aloud what the rumbling noise is, someone suggests that it's the ventilation system, to which Rennes responds "No vents." However, in the passages between rooms there are panels with ventilation slits in them (which you can plainly see even as Rennes says the line), and it's pretty impossible that the characteristically level-headed and observant Rennes wouldn't have noticed that.
Cube (1997)
1 other mistake
Directed by: Vincenzo Natali
Starring: Andrew Miller, David Hewlett, Maurice Dean Wint, Nicky Guadagni, Nicole de Boer
Revealing mistake: When they get Renn back into the room after he has been shot in the face with something acid-like, the smoke comes from behind his head. Not his face.
More quotes from Cube
Trivia: All the characters in the movie are named after famous prisons around the world - Holloway, Wren, Leavenworth, San Quentin, etc. The characters match the prison types too - Alderson never meets the group, and isolation is the major form of punishment at Alderson Prison in West Virginia. Dr. Holloway is a female doctor, and Holloway Prison is a women's prison in England, Kazan is autistic, and Kazan Prison is Russia is a "disorganized" prison, etc.
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Answer: It's established that sound travels throughout the structure reasonably well. Also, they didn't travel relatively far, even with the rooms shifting.
Actually, considering the distance that they travelled and the injuries he sustained, Quentin would have had extreme difficulty catching up. It looks like the 3 travelled upwards at least 12 cubes, meaning Quentin would have had to climb up each one with the chance that any of the rooms could be trapped fast enough to catch up to them with enough strength left over to kill Leaven.
Adrenaline is an extremely driving force, so I'd still consider it entirely possible it happened that way.