I found a four pack of 23 watt CF bulbs at Home Depot for about $9 (I wanted extras in case I screwed up). I broke the glass off the bulb leaving just the base. It was kind of a pain to get into the base where the ballast was. Once I got to it, I desoddered the wires coming from the ballast. There were two wires for power and four wires going to the bulb which was exactly what I needed. I soddered on new 18 gauge wires and hooked everything up. When I flipped the switch the bulb lit up instantly. Obviously the bulb is running at 23 watts instead of 24 watts but the difference is so small I'll never notice. You could probably overdrive the bulb a little with a slightly larger ballast (at your own risk of course).
The ballast is so small it easily fits inside the Nano Cube's hood. You could easily fit at least a half dozen inside but I don't know how you could fit that many bulbs in the hood! It's been a few hours and the hood is running cooler than another stock Nano Cube we have sitting right next to it. I doubt this ballast was designed for years of use so it may not last super long but at a cost of a little over $2 it doesn't really matter. The stock Nano Cube ballast looked pretty cheap to me so this new ballast should last at least as long, but we'll see.