The phase K3Mg20In14 was synthesized via high-temperature reactions of the elements in welded Ta tubes. The cubic crystal structure established by single-crystal X-ray diffraction means [space group Pm (3) over barm, Z = 1, a = 9.769(1) angstrom] features a 3D Mg-In network formed by K@Mg12In10 units plus cuboctahedral fillers, In@Mg-12. This is the first example of a well-ordered stuffed BaHg11 structure (Pearson symbol cP37). On the basis of tight-binding linear muffin-tin orbital, atomic sphere approximation calculations, the electronic structure of the compound shows dominant Mg-In interactions and substantial participation of Mg in the overall network bonding. Both In-In and Mg-In bondings are effectively optimized at the Fermi level. The Fermi energy cuts through substantial densities of states, consistent with the measured metallic property.