Why should Rubik's cube get attention from mathematicians?

I've seen a lot of math debate, calculations and other stuff related to Rubik's cube lately, but I don't really understand why is it important, why should anyone spend time asking and answering questions about Rubik's cube, and what good brings Rubik's cube to mathematics?

I have also found something that might be interesting, after a bit of google search. Numberphile have made a couple of videos about it, and they are quite nice:
Numberphile playlist on Rubik's cube

Solution 1:

The reason why Rubik's cube is important in mathematics is because set of all cube moves in a Rubik's cube form a group. So, it is an interesting example of finite group. You can find more information on this from this paper. Also, study of rubik's cube can lead to some interesting questions and whose solutions can in turn lead to some interesting mathematics.

Solution 2:

Often, mathematicians like to tackle a problem because it is either difficult or interesting. In the case of Rubik's cube, the associated mathematics can fall in to both categories. The necessary mathematics is also closely related to very important subjects such as combinatorics, computational complexity, and group theory, to name just three.

Also, the interplay between these subjects can often lead to interesting and sometimes surprising results. It is therefore a worthy cause to solve these problems, as the solutions can often shed light on problems in other areas that are much more applicable to real world situations (the often cited example of the role of number theory and algebraic geometry in cryptography is a good one).