If you've played Fallout 4 for even more than an hour then no doubt by now you've seen loading screens boasting the power of one Broadsider weapon, said to be a mobile cannon that allows you to blast cannonballs through your enemies. Well folks I am here to confirm the weapon does exists, and it's not hard to track down.
To obtain this item you will need to head to the east coastline, on the northern side of the river. The U.S.S. Constitution is "docked" there, a little outside the peninsula that the Brotherhood of Steel call their homebase. As you get closer, you will be approached by Mr. Handy bot named Lookout. He will engage you in a brief dialogue and induct you into the Congressional Army, which will allow you safe passage through the U.S.S. Constitution. On top of the ship is Captain Ironsides, a sentry bot with delusions of piratehood. He has a grand plan to fix the ship's rockets and send it flying out back into the Atlantic Ocean. To achieve this he will set you out on a few missions to repair or replace necessary items on the ship. You will also need to defend the ship from at least two Scavenger attacks. At one point you will be asked to retrieve an item from nearby Scavs and will need to make a choice whether to side with the humans and ransack the ship, or continue to help the robots. Side with Ironsides if you want the Broadsider.
Once all the necessary repairs are made, you will be awarded the Broadsider by Captain Ironsides. It is a unique, heavy gun that fires cannonballs. You get 24 cannonballs. Use them wisely. Save them for when you're up against Deathclaws. They punch a mean hole through Deathclaws.
Once all that's done, Ironsides will ask you to flip a switch at a nearby apartment building and from there you can watch the voyage of the U.S.S. Constitution. Enjoy!