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Depends on which dual cores and which quad cores you're talking about, and what clock speeds as well.
Not to mention, CPU power consumption isn't everything, there's also RAM, motherboard, hard drives, fans, etc.
So a quad-core system will definitely not use twice the power of a dual-core system, given that the dual-core and quad-core are at the same speeds and are of the same architecture, with the rest of the system being the same.
You should worry about the power consumption of your entire system rather than just the processor.
An i3 has hyperthreading, and the i5 doesn't. Therefore the i5 won't use double the power even if they were at the same clock speeds. An i7 might use double the power at the same clock speeds, but there's so many variables involved that it's hard to say for sure in all situations.