I think in the early years of the Roman Republic, when it was dominating Italy, at least some of Rome's conquests must have been either democracies or republics of some kind.

I know Athens attempted to invade a democratic state during the Pelopennesian War (it was their downfall.)

Also Germany was a representative republic that simply voted all the power of the legislature to the office of Leader, pre-WWII.

Its less common than either democracy/republic vs statism of some kind, but thats because historically democracies and republics have been by far the exception, not the norm.

Free countries have never waged war on each other. Capitalism (in the form of the industrial revolution) ushered in an era of peace pretty much unrivaled on the world stage for its duration and prosperity. When people are making money and their interests are in trade and production, war sounds like a pretty stupid idea. You have both moral opposition to it (we don't want to die for our country's prestiege or collective gain; we want to stay home, be productive and make personal gain,) and practical opposition (wars are risky to you personally, if you fight in it, and costly unless you are in a minority of businesses that deal with war goods; however, those businesses will always be vastly outnumbered by the businesses who will suffer net losses in paying for a war.)

With the rise of statist ideals, though, you get the rise of war. When things like national prestiege and conquest become cultural values, and when statist intervention in the economy make it harder and harder to make a living, you have both the moral argument for war (sacrifice for the glory of the motherland/fatherland/emperor/etc) and the practical hope of loot offering a rise in your standard of living, which is the only hope of such that you have in a statist economy.

Statist countries tend towards not being a Republic or Democracy, but either is possible and we've seen it before.

Democracy isn't what guarantees peace - freedom is what guarantees peace. That mistake is 1/3 of the reason we're doing so poorly in the mideast.