Is it possible to build a one-cubic-meter soundproof space? what is the minimal size of a soundproof space I could build?
A small-scale model won't produce accurate results. You will have different standing waves, resonances, and modes in small cube than an odd-shaped real-life room. Different cube-lining materials will provide a baseline relative comparison, but the results shouldn't be extrapolated to a real-life situation without careful acoustical modeling.