You'd only need one Earth's mass of computing silicon atoms and 1/4th the energy output of the Sun. It would be much more practical to try to brute force a 256-bit key in 10 years. If each device massed as much as a silicon atom, you'd end up with about 9.7 times Earth's mass. If you were to reduce it to only 1.5 million decryptions per picosecond, so light could cross one silicon atom each time, you'd need a lot more devices.
Unfortunately, light would need to be about 650 times faster to get across even one silicon atom in that amount of time. Let's say you can do $10^$ Planck time per operation, each device running at that speed would need to mass less than 69 silicon atoms in order to have enough without exceeding the mass of the Earth. That would be about $\$450$ per year for one machine. For a single server, I'll use 3741 kWh annually as an estimate. The average cost of electricity in the US is $\$0.12$ per kWh.
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