Here's this papercraft model of the 3 x 3 x 3 Rubik's Cube:
The cool thing about this model is that it is totally structurally functional like a real Rubik's Cube. In other words, you can scramble it and then speed-solve it just like you would with a real Rubik's Cube, by randomly rotating it and then applying algorithms to transform the configuration of cubies in a defined series of iterations approaching the final solved state. Anyway, on the construction of this papercraft model, the most crucial part is the central axes thingy, which allows for the rotation of center cubies attached to the axes. Mess those parts up (e.g. applying too much glue), and your cube won't rotate on those faces.
Anyway, a friend of mine has set out to construct this papercraft model and is currently procrastinating indefinitely. That's probably a wise choice. This is quite a boring papercraft models to build. You have to cut out and then glue together a bunch of structurally identical pieces: 6 parts of the central axes thingy, 6 center cubies, 8 corner cubies, and 12 edge cubies.
Instead, I have designed the following much easier and superficial Rubik's Cube papercraft model, using Metasequoia, a 3D design software. I am still just a beginner in Metasequoia, but I can see why so many papercraft designers recommended it. Perhaps I'll talk more about Metasequoia later when I have more experience with it.
Designing in Metasequoia. Nothing too fancy here. It is basically just a cube.
Here is the resulting papercraft model. This model is not functional like the one above, so carefully choose the
configuration of your cubies to glue together, for this cube won't be
doing any rotating!
Oh, but the above model is also so much work, what with a total of 54 pieces, you say? Well, here's a simplified version for the lazy papercrafters. You don't get to choose the configuration though.
Okay, here's an even lazier version for the super lazy papercrafters. Just one big piece. Yeah!! Now that's a Cube!!
You can download all three versions above here:
I don't know how to draw a visible line in Metasequoia yet, so no lines for you. You can take a black marker and divide the face into cubies if you like. Also, the physical model turns out to be 43mm x 43mm x 43mm, which is actually closer to the dimensions of a real 2 x 2 x 2 Rubik's Cube.. You can open the .pdo files in Pepakura Designer and scale them up, but then they just won't be as small and cute. So yeah, don't do that!