I love card cycles so I tried to include all possible card cycles that are in these sets in this cube.
Of course, the Khans, Charms, Banners and Runemarks from Khans of Tarkir are all in this cube (I've excluded the Ascendancies because I figured they won't be exactly what a cube card would be). But I found that there are three-couloured cards in Apocalypse that have the same colour combinations as Khans of Tarkir. They are called the Dega, the Ceta, the Necra, the Raka, and the Ana. They all have one Disciple, one Volver and one Sanctuary, which all fit perfectly into the Abzan Houses, the Jeskai Way, the Mardu Horde, the Sultai Brood, and the Temur Frontier.
Next, we have the reveal morpher cycle with
Watcher of the Roost;
Dragon's Eye Savants;
Ruthless Ripper;
Horde Ambusher;
Temur Charger.
Then we have the rare wedge-coloured creatures cycle:
Ivorytusk Fortress; Sage of the Inward Eye; Rakshasa Vizier; Ankle Shanker; Avalanche Tusker.
And the uncommon wedge-coloured creatures cycle:
Armament Corps;
Warden of the Eye;
Sultai Soothsayer;
Mardu Roughrider;
Bear's Companion.
Continuing the cycles with Fate Reforged we have the hybrid-mana activation creatures cycle with
Soulfire Grand Master; Torrent Elemental; Brutal Hordechief; Shaman of the Great Hunt; Warden of the First Tree.
And the Sieges:
Citadel Siege; Monastery Siege; Palace Siege; Outpost Siege; Frontier Siege.
And the mono-coloured 6 mana 4/4 dragon cycle:
Wardscale Dragon; Mindscour Dragon; Noxious Dragon; Shockmaw Dragon; Destructor Dragon.
The clan matter creature cycle (much like the runemarks, only on creatures):
Wandering Champion; Marang River Prowler; Battle Brawler;Hungering Yeti; Abzan Kin-Guard.
Fate Reforged also has two cycles that include modal spells (creatures and instants or sorceries):
Sandsteppe Outcast; Aven Surveyor; Hooded Assassin; Defiant Ogre; Ainok Guide.
Valorous Stance;
Fascination;
Crux of Fate;
Mob Rule;
Ruthless Instincts.
and last but not least, the Manifest Form mini-cycle from Fate Reforged:
Lightform;Cloudform; Rageform.
As you can see, these cards only contain cards from the Jeskai colours. They manifest the top card of your library and attach themselves to them when they come into play, and then grant the enchanted creature one or two relevant abilities.
Dragons of Tarkir gives us many dragons of course. And I decided to include the Fate Reforged dragonlords but to exclude the Dragons of Tarkir dragonlords. Because I think the DTK lords would be too strong in my cube. But how about some lower powered dragon cycles? Lets look at those, the first one is the Regent cycle:
Sunscorch Regent;
Icefall Regent;
Deathbringer Regent;
Thunderbreak Regent;
Foe-Razer Regent.
And guess what, morph is back in this set and even better: in the form of mega-morph. The first mega-morpher cycle is the rare megamorpher cycle:
Hidden Dragonslayer;
Stratus Dancer;
Silumgar Assassin;
Ire Shaman;
Den Protector.
The second cycle of these is the dragon tribal megamorpher cycle:
Shieldhide Dragon;
Belltoll Dragon;
Acid-Spewer Dragon;
Stormwing Dragon;
Herdchaser Dragon.
These are five uncommon 3/3 mono-colored dragons that cost {5}M, have flying, another keyword ability and megamorph {5}MM, with a triggered ability to put a +1/+1 counter on all your other dragons when turned face-up, and an additional in-color ability.
Then, to keep everything a bit in balance, we have the colour-hate cycle:
Surge of Rightousness;
Encase in Ice;
Self-Inflicted Wound;
Rending Volley;
Display of Dominance.
And the dragon matter spells:
Orator of Ojutai;
Silumgar's Scorn;
Foul-Tongue Invocation;
Draconic Roar;
Scaleguard Sentinels;
these are five uncommon monocolored cards that have an effect and an additional effect if you control or reveal a dragon card as the spell is cast.
And of course each dragonlord needs to promote himself with some propaganda, so here are the monuments:
Ojutai Monument;
Silumgar Monument;
Kolaghan Monument;
Atarka Monument;
Dromoka Monument.
And the final cycle I've included is the uncommon 6 mana 4/4 dragon cycle:
Cunning Breezedancer;
Ruthless Deathfang;
Swift Warkite;
Savage Ventmaw;
Enduring Scalelord.
Continuing with the older sets, we'll start with the enemy-coloured non-creature cycle from Apocalypse:
Soul Link,
Quicksilver Dagger,
Consume Strength,
Squee's Embrace,
Temporal Spring.
And the wedge spells from Apocalypse:
Fervent Charge; Guided Passage; Overgrown Estate;Lightning Angel; Fungal Shambler.
then, to add a little flexibility to the cube, I've also included the split cards from Apocalypse:
Night / Day; Fire / Ice; Life / Death; Order / Chaos; Illusion / Reality.
And the split cards from Invasion:
Stand / Deliver;
Spite / Malice;
Pain / Suffering;
Assault / Battery;
Wax / Wane.
Continuing with Invasion, the next cycle is the 2-mana 2/2 region creatures cycle:
Galina's Knight; Vodalian Zombie; Shivan Zombie; Yavimaya Barbarian; Llanowar Knight.
(I left out the Apocalypse 2-drops because I didn't have enough space for them in the cube)
And lastly, there is the allied-colour gold spells cycle:
Wings of Hope;
Recoil;
Cauldron Dance;
Overabundance;
Armadillo Cloak.
As you will notice, I have not included all the available cycles from these five sets. That's mainly because I didn't have enough space for those cards or that was because the cycle just contained really bad cards.