A Cube is a collection of cards, containing only one copy of each. A Cube Draft is carried by randomizing those cards into 15-card boosters and drafting them as in a normal booster draft.
This is one very simple definition for such a deep and fun way to play Magic. Cube Drafts are the best way I've found to play casually. As with limited formats, it rewards skill and does not require previous preparation from each player. It is as cheap or as expensive as you want - pauper cubes are not uncommon -, and does not require any investment from the other participants.
The fact that Cubes are composed of singletons adds great variety to the format, as happens with EDH. The much lower 40-card limit for decks, on the other hand, allows cohesive and consistent decks to be built. The introduction of similar cards in the cube will contribute to that as well.
Each Cube can be shaped to create the format that its owner wishes, in a role that resembles Wizards' R&D. The available card pool is large enough that there is a nearly infinite number of possible environments to try. Most, however, simply try to create an environment with a power level as high as possible. Also, Cubes can be sandboxes - mixing versatile and wacky cards, inviting players to design creatively -, or more archetype focused, with powerful built-in decks leading to less variety but more consistency.
Want to build your Cube and starting playing? First, you need to build the Cube. Find cards in your collection that you never got a chance play with, cards that have been good in the past but never came back to standard and are not good enough for legacy. Fill the rest with what you have that does not require a very specific deck to play. You will need 45 cards for each player, so for a full 8 person draft, 360 cards.
Don't worry too much with the first version you put together, just use the same amount of cards from each color (or not, if that is the proposal of your Cube), have around 50%-60% creatures (again, unless your Cube is not supposed to have this proportion) and you'll be fine. Stronger colors will be balanced out by more people drafting them, too weak cards won't be played and too strong cards will be apparent. As long as you and the other players have fun - and it's most likely they will - it's all good.
The material needed needed to host Cube Drafts is:
- The cards themselves.
- Basic lands: around 5 of each color for each player, which will cover occasional unbalances between colors.
- Sleeves for all cards and lands.
If you've already played a few times with your Cube and want to improve it, think about what's good about it, and what's bad. Reinforce the former, try to solve the latter. If a card is too strong, add ways to deal with it. If a strategy is too strong, take out some of the cards that add redundancy to it and make it less stable, using those slots with other strategies. Take out cards that are never played or are underperforming for other interesting ones. Add wacky cards if games are too predictable for your taste, remove them if they are too crazy.
It requires a significant time investment to start a Cube, but I strongly recommend it as a casual variant.