Theories

The Poison Theory
Why it works: In a canon comic, it is stated that Alejandro was poisoned by Cody during the Birthday Party, mainly due to the things Alejandro puts Cody through.

Why it doesn't work: Alejandro, as a ghost, tells Matt that it wasn't the poison that killed him. It was later confirmed by the creator of the Zelda Comic and the lore itself, Chekko, that the poison gave Alejandro (and everyone else who ate the cake) mild diarrhea.

How Joey Got His Teaching Degree Theory
Why it works: It has been proven that Joey is friends with a lot of magical people, so making a teaching degree with magic wouldn't be a problem (consider that he is 20 during the main events of the story, so being a teacher by legal and normal means would be impossible).

Why it doesn't work: It works.

The Pillow War Theory
Why it works: In a canon comic, Cody and company had a pillow war to decide who got the cake. Perhaps Alejandro was killed by a pillow. Sure, a pillow may not be as blunt as, say, a hammer, but perhaps he had hidden some other things in there to harden the blow... This theory could be supported by the fact that Alejandro is possibly rude to Cody at school, which would explain his motivation to kill him.

Why it doesn't work: Like stated earlier, pillows are not very blunt, and it's not possible to kill someone with one. If he was to add some other things to harden the blow, how did he get them, and how come his parents never noticed? And also, how come Alejandro was the only one killed? It is possible, however, that he targeted Alejandro specifically when making hard hits.