The response of arrays of magnetic nanoparticles (MNPs) of cubic anisotropy materials (magnetite or iron) to high-frequency (sub-GHz) field is investigated utilizing micromagnetic simulations. Composites of MNPs embedded in dielectric media are of interest as core materials for high-frequency power microconverters with low eddy-current losses. Going beyond the macrospin approximation for MNPs (including internal spin structure), we simulate the magnetization dynamics of arrays of spherical and periodically arranged MNPs under periodic boundary conditions and in the presence of thermal fluctuations of the magnetization within the stochastic thermal field. Analyzing the dependence of the dynamical response on the size of the MNPs, we find the size to be crucial for exciting regular magnetization oscillations at room temperature and reducing hysteresis loss. The efficiency of the dynamical response of composites of high-magnetization-metal (iron) MNPs is compared to that of magnetite nanocomposites. We find the sub-GHz susceptibility of magnetite-containing nanocomposite to be comparable to that of the iron MNPs despite the lower saturation magnetization of Fe3O4, (at the volumetric ratio of the magnetic phase of 0.13, susceptibility is χ≈1.6 for 5 nm Fe and ≈1.4 for 12 nm Fe3O4 MNPs at T=300 K and frequency of 0.1 GHz).