We present a numerical study based on a Monte Carlo algorithm of the magnetic properties of a mixed Ising ferrimagnetic model on a cubic lattice where spins s 1a2 and spins S 0Y 1 are in alternating sites on the lattice. We carried out exact ground state calculations and employ a Monte Carlo simulation to obtain the finite-temperature phase diagram of the model. A compen- sation point appears when the next-nearest-neighbor interaction between the spins s 1a2 ex- ceeds a minimum value. We found a strong dependence of the compensation temperature with the interactions in the Hamiltonian, particularly the crystal and the external field. An applied field can change the range of values of the compensation temperature from zero up to a maximum value that depends on the field.