The Roman conquests in many cases payed for themselves because conquests were accompanied by mass looting and exploitation of newly taken territories by the Roman army and state. An example would be slaves and the enslavement of conquered peoples following nearly every Roman conquest: Caesar for instance reported that after the conquest of of the Aduatuci tribe in Gaul he captured nearly 53,000 men, women and children of the tribe and sold them into slavery to merchants accompanying his army. Cicero however, complained that such slaves were of low worth because of their low skill and illiteracy. Caesar's armies also levied their food needs upon both conquered and allied tribes in Gaul.

More lucrative conquest target was that of Asia Minor and Greece. The long history of states in the region meant that it had some of the most developed taxation and economic network in the classical era. Sulla's soldiers in 85 BC, upon hearing that their commander had concluded a peace with Mithridates were bitterly disappointed because peace derived them the chance to loot the riches of Asia even if it meant they did not have to fight. Sulla also billeted his men in various cities in the region so he would not have to pay for their upkeep.

Roman governors in the region would practice extremely exploitative extraction of Asia minor. For instance, they would levy ruinous demands of taxes and tributes from cities, and then when they are unable to pay impose high rates of compounding interests on their debts. This would often drive cities into bankruptcy and allow the Romans to raid their assets. A substantial percentage of the population of Asia were sold into slavery to Rome and they were highly valued as educated teachers, doctors and clerks. The cruelty of Roman tax collector were in fact, was largely what led to the much of the cities of Asia Minor siding with Mithridates over Rome during the Mithridatic wars.

In Greece the repeated wars of conquest produced mass looting of valuable artwork and other pieces of Hellenic heritage to Rome. Different goods looted were "recycled" into Roman society in different ways. For instance art looted from private homes were sold to private individuals. We can see from that the ruins in and around Pompeii contained a large number of of Greek sculptures in the home of the wealthy most likely taken from Greece during the conquests of the preceding years. It is estimated that in the first great round of Greek conquests from 229-167 BC perhaps 70 million Denali (estimated to be worth $70 billion) were brought to Rome. The conquest of Macedon in particular was so profitable that the Romans were able to dispense with collecting land taxes from its own citizens in Italy for a number of years. The subsequent rounds of conquests of Greece and the East brought in much more and flooded Rome with wealth from abroad.

The Roman conquests were in other words, at least on the short run, often profitable endeavors and a large reason for those conquests were precisely the chance to loot and profit from the conquests. The redistribution of wealth from the rest of the classical world into Rome was one of the single most important economic dynamic in the antiquity. Note that Rome would not be the only state to attempt this in history, Nazi Germany and Napoleonic France are two other examples in which the state paid for their conquests largely through looting occupied territories. On the long run however, plunder eventually dries up and the real cost of defending and administrating the territories start to weight heavily on the empire.

Source:

The Cambridge Companion to the Roman Economy edited by Walter Scheidel

The Roman Empire: A Beginner's Guide By Philip Matyszak

Caesar's Gallic Wars 58-50 BC By C M Gilliver, K. M. Gilliver

A Companion to the Roman Army edited by Paul Erdkamp

Taken at the Flood: The Roman Conquest of Greece By Robin Waterfield

Sulla: The Last Republican By Arthur Keaveney