According to the evidence I gathered it seems most logical that the culprits of this "crime" were: Bowser Jr., Wario, Waluigi and Yoshi.

Various partygoers witnessed these four leaving both the Kart races and the Mario Party games, and curiously enough, Yoshi and the Wario brothers both incriminated themselves in their testimonies. They also seemed to try to incriminate the Mario brothers, most likely either out of spite from getting fouls (Yoshi and Bowser Jr.) from Mario in the Basketball games, or because of their long dated rivalry (Wario brothers and Bowser Jr.).

However, the decisive pieces of evidence were:

- All of the suspects had poor results in the Kart races, supporting the testimonies that stated they left at some point.

- The Tennis rackets with bits of frosting, whose owners are most likely the suspects, due to their respective colors and style. Green = Yoshi; Purple = Waluigi; Yellow = Wario; Red with spikes = Bowser Jr.

- The markings on the frosting of what was once the intact cake, which belong to partygoers who either possess thick fingers, gloves or claws. Yoshi's fingers are relatively thick, both Wario brothers wear gloves and Bowser Jr. has claws.

- The shoe markings that lead to the pile of frosting bearing resemblance to Mario's shoe soles. These most likely belong to Yoshi's shoes, which are more similar to Mario's than the other ones', since the Wario brothers' shoes are smaller and have pointy tips, and Bowser Jr. doesn't wear shoes at all.

As for the order of events:

- According to Toad 2, the cake was missing from 1 to 3 PM, which is when the Kart games took place.

- According to Toad 3, the cake was still missing from 3 to 5 PM, which is when the Mario Party games took place.

These suggest that the suspects stole and hid the cake when they left the Kart races and ate it during the Mario Party games, leaving the bits of frosting behind when passing by the castle. The fact their Tennis rackets had bits of frosting supports this, since the Tennis games took place after the Mario Party games.

- Toad 5 found the planted false evidence from 7 to 9 PM, which is when the Basketball games took place.

As stated previously, the shoe markings that lead to the planted pile of frosting are most likely Yoshi's, and the fact he was given a foul by Mario during the Basketball games supports the idea that he was the one responsible for planting the false evidence out of spite.

As for the motives for stealing and eating the cake in the first place: the Wario brothers and Bowser Jr. are known selfish troublemakers, so it's to be expected they'd cause mischief. As for Yoshi, he's known for his rather strong appetite. Therefore it's likely he just couldn't get a hold of himself.