A triple-barreled cannon seems to have existed in the mind of Leonardo Davinci and really nowhere else. Naval cannon could weigh as much as a ton each, so the mechanics of moving and firing a three-ton piece would have been difficult, to say the least.

It's worth noting that multi-barreled pistols existed, though they were not common. The expense of making them, coupled with the chance of misfire (flintlocks are NOT neat weapons) made them impractical.