A fuel/air explosive doesn't have to be a proper device made at a licensed munitions factory. I won't go into details, but as bombs go, they're very potent, not exceedingly complex, and don't require the use of aircraft. Every gas explosion is an example. I'm weak confidence in aerial delivery for Nashville, but higher than even on the primary target being underground with a second, ground level explosion to serve as public cover for the subterrean detonation.
I just showed a military FAE for illustration…personally I suspect that the packages were customized for the intended effects and seemed to have been well done.