Auxetic materials have been extensively studied for their design, fabrication and mechanical properties. These material systems exhibit unique mechanical characteristics such as high impact resistance, shear strength, and energy absorption capacity. Most existing auxetic materials are two-dimensional (2D) and demonstrate half-auxetic behavior, characterized by a negative Poisson's ratio when subjected to either tensile or compressive forces. Here, we present novel three-dimensional (3D) auxetic mechanical metamaterials, termed coupling chiral cuboids, capable of achieving negative Poisson's ratio under both tension and compression. We perform experiments, theoretical analysis, and numerical simulations to validate the wholly auxetic response of the proposed coupling chiral cuboids. Parametric studies are carried out to investigate the effects of structural parameters on the elastic modulus and Poisson's ratio of the coupling chiral cuboids. The results imply that the Poisson's ratio sign-switching from negative to positive can be implemented by manipulating the thickness of Z-shaped ligaments. Finally, the potential application of the coupling chiral cuboids as inner cores for impact-resistant sandwich panels is envisioned and validated. Test results demonstrate a remarkable 49.3% enhancement in energy absorption compared to conventional solid materials.