A friend of mine, while serving his prison sentence, claims he was able to build his calf muscles by carrying heavy buckets of water up and down the stairs. Is this possible?
Yes, it's entirely possible.
The main function of the calves (Gastrocnemius and soleus) is to plantar flex (point) the feet.
So, as you step up, you dorsiflex your foot slightly, then push up with your thighs and calves to elevate to the next step. Do this over and over, and you will build solid calves.