The lack of precise measurements of the ball's weight and diameter limit us to logic-based speculation on what can be seen in the photo, and comparison with cannonball types known to have been found in the Atlanta Campaign.
About the guesses that it is a Bormann-fuzed roundshell:
A Bormann fuze is approximately 1.6-inches in diameter. Study the size of the plugged hole in the Atlanta ball and compare it with the ball's width. If that is a 1.6"-wide hole, the ball would have to be at least a 32-Pounder (6.4"-caliber) ball. The only 32-pounder roundshells ever found at Atlanta were wooden-fuzed... which had a smaller fuzehole than a Bormann. For those reasons, I believe it is not a Bormann-fuzed roundshell.
The plugged hole does resemble a Sideloader Case-Shot's lead sideplug. However, that type of cannonball was EXTRAORDINARILY rare in the Atlanta Campaign. (I know of only two Atlanta Campaign Sideloaders, out of the many thousands of cannanballs which have been found there.) So, the statistical odds weigh enormously against this ball being a Sideloader Case-Shot.
Also, a Sideloader Case-Shot's copper fuzeplug (or, its empty fuzehole) should be visible if this ball is a Sideloader. Logic suggests that if this ball has a fuzehole AND a lead-filled sideplug hole, the photographer would have shown both of them. But only a plugged hole is shown.
At this point, having only the single photo and no size-&-weight measurements, I lean toward this ball not being not a cannonball. The Atlanta History Center's Gordon Jones has been mentioned as being aware of this ball. I hope one of this forum's Atlanta-area members who knows Mr. Jones personally will contact him and urge him to get precise weight and diameter measurements of this ball... which will reveal whether it is or isn't a cannonball.
Regards,
Pete