Since the Romans were losing tens of thousands of men during the war, how could they raise armies consisting of tens of thousands of men after devastating losses like Cannae ? What percentage of the eligible male population died during the war?
The whole thing about Rome's population is pretty debated with scholar's on either side with low or high counts. It'll be difficult to get a straight answer on this. The figures are for the Augustan period but give you a general idea - Brunt and Hopkins extrapolate a population of 4.5 million in Italy while the high counters (like Lo Cascio) say 13 million. You can see from that gap that what scattered data there is can be interpreted in many ways.
However, one thing to remember about Rome's casualties is that they're being split with all of Rome's allies as they made up roughly half of the field armies.
Also, it's not so much the population of Rome but the surrounding countryside. Traditionally there's always been a lot of over-population in the countryside so, there was a surplus of manpower for Rome itself to draw upon.