The biggest nuclear bombs release an energy on the order of 100 megatons: http://en.wikipedia.org/wiki/TNT_equivalent
A big earthquake is several gigatons: http://en.wikipedia.org/wiki/Richter_magnitude_scale
A nuclear bomb exploding at the center of the earth (assuming you could get it there, which you obviously can't) would therefore have less effect on volcanoes, etc., than a big earthquake, for two reasons:
- it's much weaker, and
- it's much farther from the crust, which is where the volcanoes, etc., are.
Factor 2 is such a huge effect that you wouldn't even be able to feel the explosion at the earth's surface, which is 6000 km away from the center. This is true for exactly the same reason that a person in New York can't feel an earthquake in California, thousands of km away.
This is all assuming a single bomb, which is what the OP's question asked about. I also assume that we're talking about bombs that actually exist, rather than hypothetical, more powerful bombs that might exist in the future, since otherwise the question becomes impossible to answer. (Even if you used the US's entire present nuclear arsenal, which is on the order of 100 gigatons http://en.wikipedia.org/wiki/Nuclear_weapons_and_the_United_States , it would only be the equivalent of about a Richter 10.5 earthquake. This would be stronger than any earthquake ever recorded, but it would still not produce perceptible effects at the surface, due to the second of the two factors listed above.)