It goes one of two ways, the most logical one is that even the Nazis abandon their beliefs and go "Oh so nukes are a thing... We should probably get to work on that". There is also the possibility of the Soviet disinformation campaign (depending on how convincing it was) making the Nazis think the Nuclear bombings are some sort of elaborate ruse (maybe assuming the Allies have access to thermobaric weapons or something) to scare them, but I think even the Nazis are smarter than that. The Allies are probably going to have to ramp up an atomic bombing campaign to try and bring the Reich to it's knees before they develop their own.
Interesting side affects are that Japan might surrender early, but then again without the USSR invading Manchuria I dont know if that's on the cards. Early Japanese surrender might prompt the Allies to be more aggressive with their nuclear campaign as Japan doesn't go through the whole starvation thing and swing Allied public opinion against causing mass civilian casualties.