Cube

A man named Alderson awakens in a cube-shaped room with a hatch in each wall, the ceiling and the floor, each of which leads to other cube-shaped rooms, identical except for their color. He enters an orange room and, without warning, is killed by a trap.
In another such room, five people â Quentin, Worth, Holloway, Rennes, and Leaven â meet. None of them knows where they are or how they got there. Quentin informs the others that some rooms contain traps, which he learned by nearly being killed by one. Rennes assumes each trap is triggered by a motion detector and tests each room by throwing one of his boots in first. Leaven notices numbers inscribed in the passageways between rooms. Quentin recognizes Rennes as "the Wren", an escape artist renowned for getting out of jails. After declaring one room trap-free, Rennes enters and is killed when he is sprayed with acid. The others realize that there are different kinds of detectors, and Quentin deduces that this trap was triggered by heat.
Quentin believes each person has a reason for being there. Leaven is a mathematics student, Holloway a physician and conspiracy theorist, and the surly Worth declines to talk about himself. Leaven hypothesizes that any room marked with a prime number is a trap. They find a mentally challenged man named Kazan, whom Holloway insists they bring along. When Quentin nearly dies in a room deemed safe by Leaven's calculations, tensions rise due to personality conflicts and lack of faith in Leaven's system. Quentin provokes Worth into an argument about finding the exit, and Worth accidentally reveals that he has knowledge of the Cube. Worth admits that he designed the Cube's outer shell for a shadowy bureaucracy and guesses that its original purpose has been forgotten; they have been imprisoned within simply to put it to use.
Worth's knowledge of the outer shell's size allows Leaven to determine that each side of the Cube is 26 rooms across and that there are 17,576 rooms in total. She guesses that the numbers indicate the Cartesian coordinates of the rooms. The group moves toward the nearest edge as determined by her theory, but each of the rooms near the outer wall are trapped. Rather than backtrack, they travel silently through a room with a sound-activated trap. After Kazan makes a sound and nearly causes Quentin's death, Quentin threatens Kazan. Holloway defends Kazan and provokes Quentin into an argument by calling him a Nazi. The acrimonious argument escalates until Quentin slaps her, further increasing tension within the group. When they reach the edge, Holloway scouts the gap between the Cube and its outer shell, but slips during a violent quake; Quentin initially saves her, but then lets her fall to her death and reports it to the others as an accident.
Quentin attempts to persuade Leaven to abandon the others with him and makes a sexual advance, but she rejects him. When Quentin becomes aggressive, Worth intervenes; Quentin beats him savagely and drops him through a floor hatch. Worth laughs hysterically at what he finds â Rennes's corpse. The group is demoralized by the thought of having been wandering in circles. Worth realizes that the rooms move periodically through the Cube, and this is the source of the quaking. Leaven deduces that traps are not tagged by prime numbers, but by powers of prime numbers. Much to Quentin's surprise, Kazan reveals himself to be an autistic savant who can quickly do prime factorisations mentally. With Kazan's help, Leaven guides them to a bridge room which will lead them out of the maze in two movements. Worth preemptively ambushes Quentin and leaves him behind, though Worth declines to leave the Cube, as he has lost faith in humanity.
Leaven objects and convinces Worth to join her, but Quentin reappears, kills her, and mortally wounds Worth. As Quentin moves to kill Kazan, Worth expends the last of his strength to grab Quentin's leg, pinning him in the passageway as the rooms shift again. Quentin is torn apart, and Worth dies seconds later, next to Leaven. Kazan slowly walks into a bright light.

Question: How many rooms are there in total in the Cube?
Answer: 17,576