No other details ? Lunenburg Mass ? Not any Civil War activity there that I'm aware of. Where was it found ? A quick guestimate of size going by the curvature of the fragment you're holding puts the size of the "cannonball" about equal to the size of a VW Beetle...
You didn't give us any size measurements, but comparing your exploded cannonball fragment with the width of your hand in the photo, it appears to be a fragment from a 12" or 13"-caliber Colonial Era mortar roundshell. It has to be from a mortarshell because there were no "long-gun" cannons of that caliber which got used in North America during the Colonial Era.
Your fragment appears to have a raised letter "A" marking on it. (It is not the British "Broad-Arrow" marking.) I am not as familiar with European cannonball markings as I am with American ones... but, assuming you found it in Canada instead of Massachusetts or Virginia, I think the raised "A" marking represents a French arsenal's foundry.
All really good information, and I've found it in Nova Scotia. It's a inch and a half thick. And when I traced it all the way around it was exactly 12"