They are definitely not sets, editions and more resemble Game Format since cards get in and get out.
What are the Cubes exactly?
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2Are you asking what "cubes" are in MTG in general, or are you asking specifically about what is in those particular cubes? – GendoIkari Oct 11 '16 at 14:01
In general 'Cube' is a Magic format where a person creates their own custom draft environment, choosing which cards are included. They can take cards from any sets the creators choose and can have any sort of theme their creators choose.
The Legendary Cube is one such cube created by Wizards of the Coast that is meant to showcase Legendary Creatures. Originally every creature was legendary, though it has since been updated to include non-legendary ones too. Also it was used to release some cards from various Commander products that hadn't been released in digital form yet.
The Vintage Cube (previously known as the Holiday Cube due to only being available around December) is another cube developed by Wizards of the Coast that is designed to be a 'power cube' or a cube that has many of the most powerful cards ever released in the game. This cube doesn't really have a rotation like Standard, but they do change the cards in it slightly in order to add cards from new sets and vary the environment slightly.
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1It's also worth noting (but not worth enough for its own answer) that you don't get to keep cards you draft in a Cube (paper or digital). This lets people play with cards they otherwise would have to spend inordinate amounts of money on, and lets every card in the cube be ridiculous instead of a small subset. – monoRed Oct 11 '16 at 20:21
