Flat boron has recently emerged as a fascinating concept in cluster science. Here we present computational evidence for the quasi-planar all-boron aromatic B-36 (C-6v, (1)A(1)) and B-36(-) (C-2v, (2)A(1)) clusters, established as the global-minimum structures on the basis of Stochastic Surface Walking (SSW) searches. The energetics for low-lying isomeric structures are evaluated using the validated density-functional method at the PBEO0/6-311+G* level. Our global-minimum structures are in line with a recent report (Z. A. Piazza et at, Nat. Commun., 2014, 5, 3113). These structures consist of two-dimensional close-packing boron with a perfect hexagonal hole at the center, which may serve as molecular models for the monolayer boron cc sheet. Chemical bonding analysis indicates that B-36 and B-36(-) are all-boron analogues of coronene (C24H12), featuring concentric dual pi aromaticity with an inner pi sextet and an outer pi sextet. The hydrogenated B36H6 (C-6v, (1)A(1)) model cluster shows similar bonding properties, which possesses concentric triple aromaticity with inner pi, outer pi, and outer sigma sextets.