How does a rubix cube work?

Question

For example, how do the sides become attached and unattached to the centers without coming off?

Answer 1

It is actually quite simple. The squares that are on the canter of each face swivel on a screw attached to the 6 way tee. The edge pieces slide along a circular track formed by the adjacent pieces. The corner pieces have a protrusion that holds them in the track. Take away any one piece and the entire cube will fall apart.

Answer 2

You really need to take one apart to see.
Twist the top face 45 degrees.
Use a screw-driver to pry out the edge cubes.
Then four corner cubes will fall out easily.
Once one face has been removed, you can easily twist the other four faces and remove the cubes.
In the end you will have the central structure that holds the Rubik's Cube together along with 20 little disembodied "cubicles".
If you do this, it will be very apparent how the whole thing holds together.