Specific Color Pair Archetypes:

This is the strongest deck in the cube.
Okay that's a bit harsh right out of the gate. Calling "Azorifacts" the best archetype in the cube is reductive. But it's probably the scariest. Out of the two cycles at Uncommon (the Restless lands, and the Legends), has the best of each, with both Restless Anchorage and Master's Guide-Mural being justifiable pack one pick one's. A well-built pile will reliably drown their opponent in a sea of value, so to play this archetype well, a canny drafter should watch out for the cube's abundant supply of 2-for-1s.
decks play a longer game, so watch out for cards that 2-for-1 with the Craft mechanic. Notable is Oteclan Landmark, being both an early hand-sculptor and a flyer that can jump a threat later on.

No surprises here, the deck in the two most "control"-y colors is a Control deck! Drafters looking to profit in this archetype should focus on taking early interaction and removal quite heavily. Spells like Song of Stupefaction mill yourself (counts as descending), and just neuter an opponent's threat. Don't worry so much about picking up permission: there's only four cards in the cube that counter a spell, and they're mostly conditional. Out of Air, if you pick your targets, is an on-rate counterspell. Confounding Riddle is probably your best bet, at 3 mana. And Hurl into History... Well I've never seen anyone resolve it yet...

Rakdos Aggro but this time you're doing shenanigains! Key cards include Dead Weight, a cheap removal spell that turns on Descend and hits a remarkable amount of blockers; and all-star Deep Goblin Skulltaker as a fantastic grow threat. Remember that putting landcyclers into your bin counts as descending, so maybe consider holding up that Rampaging Spiketail until you have a payoff set up?

Welcome to the easiest archetype to draft!
Gruul do be doing Gruul things. This is truly the most "brainless" of archetypes. Open Dinosaurs, draft Dinosaurs, play Dinosaurs, profit. Every relevant Green bomb has the word "Dinosaur" in it somewhere. Pick up your dorks in Poison Dart Frog, and between 0 and 2 combat tricks in the form of Malamet Battle Glyph and then just play all your dinos.
... what, you want more? Okay. Well what if I told you that all of the landcyclers are also Dinosaurs. All of them, even the ones. And if you're super lucky, you could get Gishath, Sun's Avatar and using support like Huatli, Poet of Unity or Soaring Sandwing, push into Naya. You're good for it, you've got the fixing, just run a Plains. Spice up your life, if you're so inclined...

Selesnya was kinda shafted in LCI booster draft, but I did see people smash face with Sovereign Okinec Ahau and just sort of ride that to victory. Sadly this is another archetype defined by opening a very specific mythic in Pack 1, but there's buildable synergies here. Kinjalli's Dawnrunner has double strike, so obviously holds a +1/+1 counter really well. You're playing a low-to-the-ground aggro/creatures-and-combat-tricks strategy, so pick up a Family Reunion or Malamet Scythe to goozle your opponents, and play with your life as a resource: your threats are probably better than your opp's in the late game, so trading creatures early on isn't the most advantageous.

It's a glorious time to believe in the Holy Work of Our Saviour Aclazotz, Progenitor of Vampires and Bringer of the New Dawn. Vampires are eating good with all the best removal and interaction in the cube. Dusk Rose Reliquary stands out as a sacrifice outlet and removal spell both. Vanguard of the Rose is a sac outlet that attacks and trades up most of the time. Greedy Freebooter dies very well. Mephitic Draught draws two cards! And Tithing Blade... Oh Tithing Blade, how I adore thee and thine multiple uses. It's an artifact, it's an edict, it can be sacrificed, or in a pinch it can turn into a control wincon! Load up on Acolyte of Aclazotz and Bitter Triumph and drain your opponent to victory!

Decay exists as an extant form of life. And The Mycotyrant is about as extant as life gets. Death abounds. Play a midrangey strategy, take creatures with good keywords, and dip into Black's removal for things like Chupacabra Echo. Take good creatures and turn them sideways. Malamet Veteran puts in work as the top-end of your curve, and of course Akawalli, the Seething Tower passes the vanilla test as a 3-drop and just gets better the more you feed your bin.

Fish needed some love before the patch. Pre-patch, you didn't really draft "merfolk" so much as you fell into merfolk 'cause everybody was passing you Blue cards. There's an iffy density of merfolk in the cube and you've got to be taking them quite aggressively to benefit from the synergies. Post-patch, Hakbal of the Surging Soul is among the most justifiable multicolor p1p1s. Sure, "open Hakbal" isn't exactly the most reliable strategy but he does, in fact, fuck.
Like Dino Nuggies, Fish is a linear drafting experience that rewards aggressively taking typed creatures. Unlike Dino Nuggies, you have basically no inevitability and your curve ends at 4. Tempo is your friend and your hand should never be empty; draft draw like Ancestral Reminiscence or Chart a Course. This deck is probably the best deck for Contested Game Ball, if there ever was one.

Take Abrade. Take it very, very highly. Because your whole deck folds to Abrade and if you've got it nobody else can resolve it against you. Play aggressively, run loads of 1- and 2-drops, and remember that Pirate Hat can turn any Goblin Tomb Raider into a 3/3 that can sculpt your hand. Most of the weenies in are typed pirates, but keep a special lookout for Spyglass Siren. It not only makes an artifact on entry, but it's evasive and flies!

Gnoming is hard to do in this cube, and I personally suck at it. The signposts are all sort of pointing in different directions, meaning that the archetype's themes are all over the place. Caparocti Sunborn promotes a "discover" theme that is mostly missing from the cube? Collation requirements mean that there's only one Geological Appraiser and one Curator of Sun's Creation. And Zoryowa's Justice is a bit of a trap; it can't hit tokens so its utility is limited.
My advice is play an aggro deck with an artifact subtheme. Sunshot Militia is a real card that will just kill your opp at sorcery speed if they manage to present a blocker. And you can do the Tangle Wire trick, tapping your equipment and noncreature artifacts to eke out a little more damage.

The most obvious "Secret Archetype" in this cube is the Caves deck. This is, ofc, by design. Booster packs of LCI had a chance to contain basic lands instead of Caves in the lands slot, but it's obviously pointless and bad in a cube to put basics in packs. So I made a Caves slot.
The upside is that There's One In Every Pack. You'll wheel lots of utility and if nobody is being greedy you'll likely be alone in your lane. The downside is that your card quality suuuucks. Every Cave you take could have been a bomb, or a removal spell, or a creature that blocks.
Remember to look out for the "secret" cycle of Uncommons that care about Caves: Bat Colony, Sinuous Benthisaur, Gargantuan Leech, Calamitous Cave-In and Spelunking. You might notice poor Benthisaur doesn't do much more than draw you two cards, and is a well-below-rate creature on top of that. isn't exactly the best color for the Caves deck, even for an ostensibly "five color" archetype. This deck most comfortably rests as a 3-color midrange pile. But don't let your dreams be dreams! Draft that Cosmium Confluence pack-1-pick-1, take Scampering Surveyor pick 2, and pray someone ships you a payoff!

One Final Note

This list is not exhaustive, and definitely not doctrine. If you want to experiment with weird archetypes and try to make them work, go for it! Wanna play Discover? What about Fliers? Maybe Midrange? Go crazy! This cube is a toy, and the only reason I pull it out is to have fun with my friends and occasionally resolve Hit the Mother Lode. The points are made up and the scores don't matter, so take cards you like and want to play with. I'll see you at the draft, but until then: good luck, have fun!