Big Red has an interesting history in cube. It evolved as a copy of Kai Budes 1999 world championship deck as a response to the popularity of a red blue version using Tinker, Upheaval and any other blue power it could pick up. By focusing on picking up the artifacts and land rather than the blue cards you could undercut anyone else trying to draft what was at the time considered to be the best archetype. You could then pick up a few useful red spells to fill out the deck late as Wildfire (to replace Upheaval) would often be floating round towards the end of boosters. Wheel of Fortune would also often end up going late due to the lack of homes for it.
Goblin Welder is one of the most powerful cards in magic but to abuse him you need an appropriate deck. The red blue versions wanted Welder as much as Tinker as they had better ways to abuse than a mono red deck due to the discard on Thirst for Knowledge and Frantic Search. Big Red is the second best home to power up a Welder and it recently improved a great deal with Faithless Looting and while perhaps not quite as abusive as the red blue version it is still one of the best things about this deck.
As such Big Red is a mash of three different things that has been both fun and powerful enough to be a cube mainstay throughout my cubes life time (Mirrodin Block). A copy of a succesful constructed design, a counter strategy for an over drafted powerhouse and a vessel for Goblin Welder to abuse from. It is also one of the only other decks you can build that is half decent and mono red other than red deck wins. In addition to this it is one of the only places you can play with big dwagons and fireballs and not lose horribly. Below is a very generic list of what Big Red tends to look like in its current evolution. I have included a large list of cards that frequently see play in Big Red that are used to tune it for dealing with various different match ups.
Chandra the Firebrand
City of Traitors
Urabrask the Hidden
Flame Tongue Kavu
More Big Reg Style Stuff
Wheel of Fortune
Other red planeswalkers
Crucible of Worlds
There are a few ways to lean with the build, you can either go very heavy on the mana denial or very heavy on the threats. Historically it always used to lean towards the mana denial as that was better against combo and control however with much better threats for Big Red to chose from and more creature based beatdown format the fast threats approach has been working very well. The main list I have offered is pretty much bang in the middle of mana denail and threats supporting only the best cards from each category. This list is just an example and has not been designed to cope with anything in particular, I doubt anything as half mast as this would not be the result of an actual cube but it does serve well to demonstrate the archetype.#
Red has never had much access to card advantage hence the prevalence of tempo decks and those with phenomenal redundancy. Big Red evades the problem of card advantage with a combination of card power and tempo. It says I am not going to get card advantage and so to hell with it, I will sacrifice further card advantage to gain a huge mana advantage and then out power my opponents with monstrous threats and large scale mana denial. This can make Big Red inconsistent and you can get opening hands with no acceleration that do basically nothing or you can draw only ramp and whimper out. Inconsistency is very bad for any deck and pretty shameful for a mono deck however most inconsistent decks don't make up for it in quite the same way. More often than seems fair Big Red will get such a fast draw that it will seem unbeatable regardless. I fondly remember a Big Red deck of old going Workshop Metalworker on turn one into Lightening Greaves and Darksteel Colossus on turn two.
Big Red is a deck that often rewards you for going all in. When presented the opportunity to do something broken early on it is usually right to risk running into that Daze. Stalling for too long allows your opponent to get a foothold in the game. Big Red wants to play the game on its own terms, either with lots of mana to none and at a steady pace or with 6/6s against 2/1s in a short space of time. It is not too hard to draft or to play, is great fun and is a tier one deck all of which make it a great cube archetype. While not being the most demanding of decks it still rewards the seasoned wizards and the tricky mages with many subtle interactions and synergies.
Big Red is neither a combo deck nor an agro deck nor a control deck but a blend of all three in fitting with its evolution. Your opening hand will likely dictate which role it will be performing and then your subsequent draws and game state will dictate when it suddenly wants to change things up and do something else. Red lacks reliable ways to deal with spells and enchantments as well as big or resilient monsters. For a mono red deck to be viable it needs to win before they can become an issue or stop the opponents from getting to do anything it wants. Big Red can do either of these things.