We employ a system of cubic colloids with rounded corners to study the close-packed monolayers that form via convective assembly. We show that by controlled solvent evaporation large densely packed monolayers of colloidal cubes are obtained. Using scanning electron microscopy and particle-tracking algorithms, we investigate the local order in detail and show that the obtained monolayers possess their predicted close-packed optimal packings, the Λ0-lattice and the Λ1-lattice, as well as the simple square-lattice and disordered packings. We further show that shape details of the cube corners are important for the final packing symmetry, where the frequency of the Λ1-lattice increases with decreasing roundness of the corners, whereas the frequency of the Λ0-lattice is unaffected. The formation of both optimal packings is found to be a consequence of the out-of-equilibrium formation process, which leads to small shifts in rows of cubes, thereby transforming the Λ1-lattice into the Λ0-lattice.