Subwavelength particles supporting Mie resonances underpin a strategy in nanophotonics for efficient control and manipulation of light by employing both an electric and a magnetic optically induced multipolar resonant response. Here, we demonstrate that monolithic dielectric nanoparticles made of CsPbBr3 halide perovskites can exhibit both efficient Mie-resonant lasing and structural coloring in the visible and near-IR frequency ranges. We employ a simple chemical synthesis with nearly epitaxial quality for fabricating subwavelength cubes with high optical gain and demonstrate single-mode lasing governed by the Mie resonances from nanocubes as small as 310 nm by the side length. These active nanoantennas represent the most compact room-temperature nonplasmonic nanolasers demonstrated until now.