We have performed a self-consistent calculation for the energy band profiles and energy levels of cubic quantum dots, solving both the Schrödinger and Poisson's equations. In particular, we examined the effect of doping on these levels both in the presence and absence of a positive test charge. We found that the number of levels the cubic dot supported depended on the size of the dot, and that the energy of the levels decreased in the presence of a positive test charge. Moreover, we found that the energy levels of both the singlet and triplet states in the dot increased with the doping density. The quasi-Fermi level was found to be lower in the presence of a positive test charge than in its absence, and the quasi-Fermi level increased sharply with increasing doping density both in the absence and presence of the test charge. With very high doping the Fermi level is located in the barrier while with low doping the Fermi level is located down below the ground state energy which implies that the probability of finding an electron in a dot is very small. We also find that at high doping levels the lowest energy states are no longer confined in the dot. The potential energy profile was found to be dramatically affected by both the doping and the presence of a positive test charge. The profile was found to become asymmetric when the test charge was displaced from the center of the dot.