@Yet One More Idiot  
It was, so I just had to do comment on it.

@sTs  

 
…they’re 687 already. And that’s why comments like yours (and mine) are so pointless, they date so quickly. :P

Oh no the likes are 666!!!

@Binkyt11  
This is it.  

Nonchalant Whistling
 

@Binkyt11  
The only to solve that, is with a scaled up version of the rublk’s cube solver mechine

If y’all think that this is hard, none of y’all haven’t seen jack shit then. BEHOLD-  

In Trixie’s defense of being puzzled by it, that Rubik’s Cube is impossible. It has two lower-left green squares so nobody can solve it :P

@Samekh  
You talking about this?
 
@Background Pony #45FC  

@Lord Seraph  
Are you sure?

I could see this happening in the show, really.  
“The Great and Intelligent Trixie will make this puzzle look like foal’s play! (proceeds to fiddle with it for the entire episode without actually making progress)”

Too cute. ;-)

Twilight makes this look easier than it really is.

@Nightweaver20xx  

 
I would imagine so - the total number of elementary particles in the universe is estimated to be about 10 ⁸⁵.  
By comparison to that, if you filled the whole universe with elementary particles, it’s estimated there would be about 10 ¹²⁰ of them.  
And the volume of the universe in planck units of volume (1 planck volume is many orders of magnitude smaller than any elementary particle currently known, and is theoretically the smallest volume it would be possible to measure) is something like 10 ¹⁸⁵ Planck Volumes.
 
Don’t worry about that cube, Trixie, we can work on that together in a while. Why not take a break from it and we’ll have some juice and cookies together, cutie-pone? :)

Looks like someone’s gone and made it better  

It’s just super cute

@Yet One More Idiot  
I believe the final number of states is more than the total number of subatomic particles in the known universe.

Wait how this image got featured?

@Nightweaver20xx  

 
Whether our physical universe contains 3, 4, 7, 12, 28 or an infinite number of spatial dimensions isn’t actually that relevant to this, as it isn’t a physical object that occupies actual space - it’s a mathematical model in a computer, and therefore as many spatial dimensions as required can be modelled. No doubt one could, with sufficient computational power and time (and if they were sufficiently bored, I imagine), code a Rubik’s puzzle with any sufficiently large number of spatial dimensions. xD
 
For more info on the Magic Cube 7D, go to the devs page here: http://superliminal.com/andrey/mc7d/
 
But to answer your original question…I don’t know how many possible states the 5^{7 cube has, but on the devs page it says that the 3}7 cube has about
 
3.37 x 10 ¹⁰⁸⁹³⁵
 
possible states. That’s a 108,935-digit number. Think about that for a second, let it slowly sink in and break your brain. xD

Trixie need her great and powerful assistance.

@Havock  
My point exactly.

@TheMultiBrony21  
We’re on 1832925 now.

@sTs  
I do. There are a lot of images on this site.

I know, right?