How much energy would be required to actively reduce the temperature of the oceans of Earth by 1℃?
The question is slightly confused, because reducing the temperature of the oceans, in a direct sense, doesn't require energy - it releases it. The amount that is released is simply related to the mass and specific heat capacity of seawater, as you suggest.

The missing question, though, is why the ocean is cooling. For it to happen naturally and simply release energy, it would need to be because its surroundings (e.g. the air) were cooler. If you want to actively cool the sea, then yes, that is going to consume energy. If the cooling has approximately the same level of performance as building-sized air conditioning, the power used by the cooling apparatus will be about 40% of the rate at which the energy is removed (and remember that this is not just the total energy divided by the time, because more heat will be leaking back in while you do it).

Leaving aside the, uh, engineering challenges of this scale of cooling, this leads to a question as to why one might want to do this. Remember that unless you devise some complex system to radiate this heat into space from above the atmosphere, you're going to be releasing the same heat into the same global climate system, plus the additional 40% that you've used to move it around.