We present theoretical calculations of the characteristics of the static magnetic response of multicore magnetic nanoparticles. These particles contain a considerable number (∼10^{2}) of single-domain magnetic nanocrystallites, which are modeled as uniformly magnetized balls with uniaxial magnetocrystalline anisotropy, the energetic barrier of which is comparable with the thermal energy. Thus, we model a multicore magnetic nanoparticle as an ensemble of superparamagnetic nanoparticles, the position and the easy magnetization axis of which are fixed but randomly distributed. Summing up the magnetic moments of the nanocrystallites inside a multicore particle, we thus obtain the magnetic moment of the multicore particle under the assumption that magnetic interactions between the nanocrystallites can be neglected. It is found that the weak-field magnetic response of these multicore particles is independent of anisotropy constant. The model is compared with recent experimental data and good agreement is found.