Rainbow dash  
she has to be because FS and RDs statements can’t both be lies, and if fluttershy’s statment were true then twilights statement would be a lie, which would make both of them guilty,and only one can be guilty. Therefore RD must be telling the truth, making twilight the liar and the thief
 
And no it couldn’t be that no one ate it like People in the comments are saying because Im this situation what the narrator says is the truth, otherwise for all we know all of them could be lying

Ok this has my brain in a twist but I think I got it. If Twilight was telling the truth, then FS, RD, and R are lying. If Rainbow Dash is lying then Fluttershy is telling the truth. Both Twilight and Fluttershy can’t be both telling the truth.
 
If Fluttershy is telling the truth, Then Rainbow would of Ate it and Twilight who is also lying, would of had to of had ate it. I think they are looking for only one pony here.
 
If Rarity is telling the truth, Then Fluttershy ate it but if Rainbow also is lying, then Fluttershy IS telling the truth and there can’t be two truth tellers.
 
Now if Rainbow was telling the truth, Then Fluttershy is lying, Rainbow did NOT eat the dessert, Rarity is lying and Fluttershy did NOT eat the Dessert, Twilight is lying and DID eat the dessert. It is the only logical conclusion. Twilight is a piggy.

@Background Pony #38BA
 
you genius.

This is pretty complicated, but I’m gonna say that Twilight is telling the truth. The cupcake is right there, so Twilight didn’t eat it.

Applejack’s gone for a reason.

@The Smiling Pony  
Nah, that cupcake is way too small to be her main course. It’s only slightly bigger than her head XD

@Badumsquish  
You’re assuming that’s Pinkie’s desert and not the main course.
 
This is, after all, Pinkie Pie.

Nobody ate the dessert. It’s still right there in front of Pinkie Pie. The only one telling the truth is Rainbow Dash :P

@The Smiling Pony  

 
Reminds me of the episode MMMystery on the Friendship Express, where Applejack ended up being the only one of the mane six besides Pinkie and Twilight who was not guilty.
 
When I was watching the episode, I was pretty confident that Applejack wasn’t one of the culprits because I had a very high opinion of her, and I couldn’t legitimately see her doing something like that. However, it wasn’t until later that I learned that Applejack was originally intended to be guilty as well, but that part of the script was cut. Yeah, I would NOT have been happy if it hadn’t been…

@Background Human  
I actually misread the original question and did 2) first. Either Rarity or Fluttershy would’ve been false, which means Rainbow was true. Therefore Fluttershy ate it.
 
I suspected 1) may have multiple answers, so I brute-forced it. Working out the logic might’ve been easier, but it’s late in the evening over here.  
T=True, F=False
 
TT  
FF = Rainbow
 
TF  
TF = Rarity
 
^ Those are the only combinations that work. The neat thing was how, depending on the question, any of the four ponies had exactly one scenario where they could’ve eaten it.

@Josh103  
Can’t happen. If Dash is telling the truth, then Fluttershy is lying, and vice versa.

@Background Human  
What if all of them are telling the truth? What if nopony was?

Bonus question:
 

Twilight.  
Flutershy lies and says it was Dash  
Rarity lies and says it was Fluttershy  
Twilight lies in denying it  
And Dash tells the truth in that Fluttershy lied

AJ needs to have a long talk with y’all about honesty. Especially you, Twilight. Princess of Fatty-Fatty-Fat-Cakes.
 
@FamusJamus  
The giant cupcake is her after-dessert. Her dessert was a regular cake-cake.

Pinkie’s dessert is pictured whole and ungobbled. Therefore the narrator is unreliable.
 
The only motivation for the narrator to be unreliable is if they relish confusing us on this side of the fourth wall with the chaos on the ponies’ side.
 
Therefore, the narrator must be Discord, which in turn makes it possible that all the ponies believe what they are saying.
 
Either that or Pinkie has more than one giant cupcake, but that’s just silly.

Rainbow is telling the truth  
Twilight ate the cupcake

@Background Pony #C72D  
Imagine the mini-shitstorm if AJ were part of this and the only logical solution had her as a liar…
 
Wonder if whoever made this kept her out on purpose.

Funny how the Element of HONESTY isn’t there…
 
Applejack ate it

There’s an easier train of thought:  
Notice that Flutters’ and RD’s statements must be one true and one false. Then, if only one of them is telling the truth, then it must be one of RD or Flutters. Thus, Twilight is lying, and she ate it.

Guys…seriously?
 
Rainbow Dash is telling the truth. The rest are lying. It only makes sense and there’s only one possibility if Rainbow Dash is the one telling the truth.
 
If Twilight’s telling the truth, that means that she didn’t do it, and Rarity’s lying about Fluttershy doing it, Rainbow Dash is lying about about Fluttershy lying, so that means Fluttershy’s telling the truth, which is impossible.
 
If Fluttershy’s telling the truth, then Rainbow Dash is the one that did it, but Twilight is lying about not doing it,  
so that makes no sense either.
 
If Rarity’s telling the truth, then Fluttershy did it, but again, Twilight’s lying about not doing it, but again,  
Twilight is lying about not doing it.
 
So, Rainbow Dash is telling the truth. Fluttershy is lying about Rainbow Dash eating the dessert, Rarity is lying about Fluttershy eating the dessert, and Twilight is lying about not eating the dessert, which means that Twilight is guilty.

Also I guess if Rainbow was telling the truth Fluttershy and Rarity were just willing to lie to Pinkie and throw their friends under the bus. So much for kindness. :P

I’m just causally watching the comments section

I’m concerned over the fact that the group has resorted to thievery now, it’s quite demoralizing. Faust would be rolling in her grave if she could see what her little ponies have devolved into (it’s a joke).

I bet that cupcake is the dessert. Dang it Pinkie it was right in front of you the whole time.