In this paper, we study the orientational texturing and static magnetization of a small multi-core particle (MCP) that includes a few immobilized superparamagnetic particles (SPPs). We focus on the consideration of the MCPs containing 7 and 8 SPPs, which are located randomly or at the nodes of a simple cubic lattice. The results are obtained using Monte Carlo computer simulations. It is shown that intensive dipole-dipole interaction leads to the formation of an orientational texturing of the SPP's magnetic moments, which strongly depends on the location of the SPPs inside the MCP. The magnetization laws of MCPs are compared with the continuous medium magnetostatics. For strongly interacting SPPs there is a big difference between the simulation results for the magnetization of the MCPs with cubic structure and the magnetization of continuous system of SPPs located in simple cubic lattice. The magnetization of the MCP for each specific random location of the SPPs also differs from the magnetization of continuous media of SPP gas, however, the average value of the MCP magnetization coincides with the continuous media magnetostatics.