Considerable recent research effort has been devoted to the development of boronyl (BO) chemistry. Here we predict three perfectly planar boron boronyl clusters: C_2v B₆O₄ (1, ¹A₁), D_2h B₆O₄⁻ (2, ²B_3u), and D_2h B₆O₄²⁻ (3, ¹A_g). These are established as the global-minimum structures on the basis of the coalescence kick and basin hopping structural searches and electronic structure calculations at the B3LYP/aug-cc-pVTZ level, with complementary CCSD/6-311+G* and single-point CCSD(T)/6-311+G*//B3LYP/aug-cc-pVTZ calculations for 2. The C_2v B₆O₄ neutral cluster features a hexagonal B₄O₂ ring with two terminal BO groups. The D_2h B₆O₄^−/2− clusters have ethylene-like structures and are readily formulated as B₂(BO)₄^−/2−, in which a B₂ core with double bond character is bonded to four terminal BO groups. Chemical bonding analyses show that B₆O₄ (1) possesses an aromatic π bonding system with three delocalized, six-centered π bonds over the hexagonal ring, rendering it an inorganic analogue of benzene, whereas the B₆O₄^−/2− (2 and 3) species closely resemble ethylene in terms of structures and bonding. This work provides new examples for the analogy between boron oxides and hydrocarbons.