The Cube series takes place in the Aperture Science Research Facility.
The two Cubes were developed or discovered by the SCP Foundation.
The Hypercube is an experimental gateway to parallel universes.
There is nothing outside the Cube.The Cube is the only real thing. The memories of being in the real world are false. The prisoners were vat grown. When you go outside, you die almost immediately. Hypercube is another dimension.
The Cube is in space.All survivors are shot out the airlock immediately. If they're particularly unlucky, they may have to listen to some poetry first.
The Hypercube is a failed attempt to recreate a TARDIS.Just think about it. It's bigger on the inside, can manipulate space, time, gravity, etc. Some time ago, humans might have acquired a broken TARDIS and then built something that was supposed to resemble it. They failed.
Each room of the Hypercube has six interiors at a time.The rooms rotate in three spacial dimensions; what's to say they don't rotate in four? This is how, before the collapse, some marked rooms seemed to contain variable contents. Whether the interiors each belong to one of six different internally consistent sets (forming the "parallel universes") or if each room has its own set of six interiors depends on how the cube was made. Simon has fewer than six of each kill trophy, so it could be either. If each room has more than 6^1 interiors, that really doesn't add any meaning to this guess other than narrowing down the possibilities of how the cube was unfolded/folded/formed/whatever. Obviously, this doesn't include the limited external room[s], since the external space in which the outside of the cube was kept seemed to be no larger than a single internal room.
Kazan knew that Quentin was going crazy.In fact, he could tell a long time before anyone else did, but he couldn't communicate it to anyone else because of his severe autism (or brain damage, depending on your theory). That's why he yelped when Quentin was still in the sound activated spike cube.
The cube is a Lament Configuration.A cube-shaped puzzle box with moving parts, which hides undescribable horrors and torrents of physical and psychological torture? Yup, I think we know what this is all about. Interestingly, note the opposition between people who solve the puzzle from the outside, hoping to reach the epitome of pain, and those solving it from the inside, trying to escape it.
Leaven was pretending that factoring prime numbers was harder than it wasShe's obviously good at maths but spent ages on the first two numbers, which ended in "2" and "5". Given she was in a group of strange people, and was probably slowest and weakest, she pretended that her task was more difficult than it really was. She only seems to actually work hard (doing equations on the walls, etc) on problems that are more challenging. If she told the other people a few of the tricks for finding divisors of large numbers, or helped them tabulate all the powers of primes less than 1000, that would probably hurt her chances of survival.
Quentin was right it was a billionaire's sick joke.Why else would the room they were looking for as a means to get out was in one of the rooms they should have stayed in the entire time.
The Hypercube is an attempt to simulate a multiverse.It's ideal for simulating it. It has a starting point that can be traced easily (The activation of the Hypercube), allows easy surveillance (Since every "timeline/world" is a single room), and there is a limited amount of elements to keep everything simple and easily traceable. Of course, it was meant to be purely theoretical and at best involve no human subjects due to the natural ethical quandaries of the situation, but someone had the bright idea of putting human subjects in to allow for that free will aspect.