A systematic numerical study of three-dimensional natural convection of air in a differentially heated cubical cavity with Rayleigh number (Ra) up to 10(10) is performed by using the recently developed coupled discrete unified gas-kinetic scheme. It is found that temperature and velocity boundary layers are developed adjacent to the isothermal walls, and become thinner as Ra increases, while no apparent boundary layer appears near adiabatic walls. Also, the lateral adiabatic walls apparently suppress the convection in the cavity, however, the effect on overall heat transfer decreases with increasing Ra. Moreover, the detailed data of some specific important characteristic quantities is first presented for the cases of high Ra (up to 10(10)). An exponential scaling law between the Nusselt number and Ra is also found for Ra from 10(3) to 10(10) for the first time, which is also consistent with the available numerical and experimental data at several specific values of Ra. (C) 2017 The Authors. Published by Elsevier Ltd.