Had the US or Russia wanted to detonate a nuclear bomb on the moon, would they have had the means to get one there? Would those bombs have worked on those conditions (vacuum, low grav, etc)? Could it have been a manned mission (dropped from moon orbit) or would it have been unmanned for cargo capabilities reasons?
Why would they want to drop a nuke on the Moon?
Meh, why wouldn’t they, orbiting us up there like it thinks it’s somebody.
Don’t fight the hypothetical. 
The US could have put on a Saturn V. The Apollo lunar module weighed around 15 tons, which is plenty big enough.
Since the dawn of time man has yearned to destroy the moon.
The Soviets couldn’t have managed a manned flight (they never even sent Cosmonauts into lunar orbit), but they did land the five ton Lonokhod 2 on the moon in 1973, and they definitely had warheads weighing less
As Tapioca Dextrin said, the U.S. could have, when they had Saturn V’s still around. We’ve made other heavy lift rockets over the years, but I don’t think they had the ability to get to the moon. The Delta IV (our current heavy lifter) won’t make it to the moon.
The Soviets were able to land unmanned spacecraft on the moon, though their Proton rockets were notoriously unreliable back in the early days of the space race. The Russians still make Proton rockets (it’s what they use to get to the ISS), so they can still nuke the moon. Coincidentally, the Proton was originally designed as a system to carry nukes, even though it has never been used for that.
It’s already happened. In 1999 a giant nuclear explosion on Moonbase Alpha pushed the moon out of its orbit and sent it hurtling on a voyage through space. (That’s a hologram we see in the sky now). 
Seriously, here’s an interesting story.
I remember seeing that documentary!
Luna 3 took pictures of the back side of the moon in 1959. The probe massed 278.5kg.
In 1965, the 960kg Zond 3 probe photographed the moon’s far side.
I expect you could build a nuke having a mass somewhere between 278 and 960kg.
Also, if you can fly something past the moon, it’s very likely you could collide it with the moon.
I hope they planned on naming the missile “Alice”.
I should think so. 960 kilgorams would be an big nuclear device. That’s more than twice the mass of the W-87 weapon used on Minuteman III missiles.
I for one fully support the detonation of the largest nuclear weapon possible on the Moon, for the reason that it would be really freaking awesome.
During the Cold War, the Pentagon really, really wanted to do this as a stunt. The US was fully capable of doing this, but since a) it serves absolutely no military purpose and b) it would forever contaminate the Moon, scientists were able to persuade the administration not to proceed.
I seem to recall some talk about using the far side of the moon to hide illegal nuclear tests from the Russians (or fear that the Russians would do the same to hide their tests from us).
Of course, a test isn’t much good if you can’t get data back about the results, and putting instruments up along with the nuke (and not having anyone notice the instruments reporting back) would be pretty dicey, so I suspect this was more Cold Warrior paranoia then a workable plan.
Carl Sagan was involved with the nuclear bomb on the moon project according to his biography.
Robert McNamara mentions the fear of the Russians using the far side of the moon for nuclear tests in The Fog Of War, that’s a googlevideo link, a very interesting film that.
When he dramatically told them how much it would cost they freaked out and immediately canceled the program
We don’t have any manned rockets capable of reaching the Moon any more, but we do certainly still have rockets that could do it unmanned. Consider that we routinely send probes to Mars and other planets, and those are at least as hard to reach as the Moon.
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How do you detect microrganisms with a nuclear bomb? You listen to the Force to see if millions of voices suddenly cry out in terror and are suddenly silenced?