The typical electron-deficiency of the boron element renders fascinating architectures and chemical bonding to boron-based nanoclusters. We theoretically predict two di-Ca-doped boron clusters, B6Ca2 (D2h, 1Ag) and B8Ca2 (D8h, 1A1g), and both adopt interesting inverse sandwich geometries, showing an elongated D2h B6 or perfectly planar D8h B8 ring being sandwiched by two Ca atoms only, respectively. Natural atomic charge analyses indicate that the Ca atoms donate nearly all the 4s electrons to the B6 (or B8) ring, forming [Ca]2+[B6]4-[Ca]2+ and [Ca]2+[B8]4-[Ca]2+ charge transfer complexes. The interaction between the two Ca atoms and the boron rings is governed by robust electrostatics albeit by weaker B-Ca covalent interaction. Chemical bonding analyses show that B6Ca2 has 4σ and 6π delocalized electrons on the elongated B6 ring, leading to a conflicting aromatic system. B8Ca2, possessing 6σ and 6π delocalized electrons on the B8 ring, is doubly aromatic. Additionally, the B6Ca2 and B8Ca2 clusters show noticeable structural and electronic transmutation relative to their equivalent electronic B6Be2 and B8Mg2 clusters, respectively. The intrinsic reasons behind the transmutations are elucidated via in-depth bonding analyses.