How Much Computing Power would be Required to Fully Simulate a Cubic Meter?
tricky question! there is some diverse crosscutting research into this question, and will attempt to outline it, but will in the end take the position here that the question is contradictory/ impossible at heart (and anticipating some this may be a controversial conclusion). here are two key recent references from a physics pov addressing your question. 


Gate count estimates for performing quantum chemistry
on small quantum computers / Wecker et al
Quantum Algorithms for Quantum Field Theories / Jordan, Lee, Preskill


a rough complexity theory estimate of "simulating particle physics" is to count the number of particles, and there are about $O(n^2)$ interactions between particles, and many supercomputer simulations of particle dynamics fit this. so as a rough bound, one would pick the smallest particles, but, wait! the standard model has many subatomic particles! so one might use neutrinos, one of the smallest known stable particles, as an estimate... but then what about unstable particles such as quarks/ leptons?

there is also the whole other problematic accuracy/ precision problem of the butterfly effect long known in computational physics aka "sensitive dependence on initial conditions".

Aaronson write in his essay Is There Anything Beyond Quantum Computing?:


  Is there any such problem that couldn’t be solved efficiently by a quantum computer, but could be solved efficiently by some other computer allowed by the laws of physics?


so he sketches out weird physics such as black holes or quantum gravity that might not be simulable by a quantum computer. but flipping this whole essay on its head (in a manner it which it was unintended), what he is describing are frontier areas of physics that currently do not have complete/ definite physical theories known by humans (at best, only plausible candidates/ approximations floating around.) eg: 


black holes
time curves
quantum gravity


(adding to his list) 


dark matter/ energy
virtual particles, vacuum energy


so the problem comes in your title that you literally want to fully simulate a cubic meter of space. but the standard model is actually ultimately/ technically widely acknowledged/ conceded by physicists themselves (if pressed!) as an incomplete model of reality due to all the extreme/ problematic "edge cases" listed above, and others not known. even the standard model itself is problematic in that new particles/ tiny forces and revisions are added/ modified all the time, nearly "regularly", even the famous/ celebrated Higgs particle recently.

so actually its a major open question of physics whether the basic rules of reality are computable. this ties in with the digital physics research agenda.

so physicists generally regard the idea that physics of reality is computable as something of an "approximation" that physical theories are in the continual process of evolving/ finetuning but "very thorough/ precise models" are ultimately not to be confused with accurate simulations.

also relevant to this question/ impinging is that there is new "cutting edge/ borderline" physics theory/ research and experiments to attempt detect if we are "living in a hologram" ie some kind of "simulation". it is theorized that cosmic rays might have detectable properties indicating this, or other very sensitive experiments could reveal kinds of "digitization artifacts", etc.; one example:


The Measurement That Would Reveal The Universe As A Computer Simulation / MIT tech review