Rome pairs a genuine Culture engine with one of the strongest militaries in the Antiquity Age — its Legion gets stronger for every Tradition in your government, not just from combat experience.
"Twelve Tables" increases Culture in Districts in the Capital and in City Centers in Towns (this bonus increases further once Rome reaches the Modern Age as a Time-Tested civ), and grants a free Infantry unit every time you found a new Town. In its Antiquity Age Apex form specifically, it also adds Production toward Military units in the Capital for every Town you control, and training an Infantry unit grants Culture equal to a percentage of that unit's Production cost.
The Legion is a unique Infantry unit that gains +2 Combat Strength for every Roman Tradition currently active in your government — with all four Traditions unlocked, this makes it one of the strongest land units of the Antiquity Age. Rome also has a unique Commander, the Legatus, who can gain the ability to found a new Town outright after enough Promotions — a genuine alternative to building Settlers if you keep it in active combat.
The Forum is a Unique Quarter created by building Rome's two Unique Buildings — the Temple of Jupiter and the Basilica — together in the same district. Unique Quarters like the Forum are Ageless: once built, their effects persist through every later Age of the campaign, and nothing can be constructed over them. Rome's associated Wonder, the Colosseum, also gets a +30% Production bonus when Rome builds it, and grants a unique Narrative Event choice when completed.