Due to the strain gradient near each surface of a BaTiO3 nanocube in their ordered assembly, electric polarization appears due to flexoelectric effect. The magnitude of the flexoelectric polarization could be one order of magnitude larger than that of ferroelectric spontaneous polarization of BaTiO3. Thus, dielectric response of an assembly could be dominated by that of the flexoelectric polarization if there is no ferroelectric domain-wall motion. Numerical simulations of the dielectric response of a BaTiO3 nanocube in an ordered assembly are performed from kHz to MHz range based on a dynamic model of flexoelectric polarization assuming anharmonic potential. The calculated temperature dependence of the dielectric constant is consistent with the experimental data of high dielectric constant with nearly-flat temperature dependence. It is suggested that high dielectric constant with nearly-flat temperature dependence is not originated in ferroelectric nature of BaTiO3 nanocubes but originated in flexoelectric polarization in nanocubes which is also seen in non-ferroelectric materials.