Trivalent europium (Eu3+) has an anomalous magnetic behavior at low temperatures because its first magnetic state is removed by approximately 500°K from the nonmagnetic ground state. The effect of a crystal field or a europium-iron (Eu-Fe) exchange interaction on the energy of the ground state is the result of the partial breakdown of the LS coupling caused by these perturbations. We calculate the first-order cubic anisotropy constant K1 for the ground state of Eu3+ in europium iron garnet (EuIG) due to the combined action of the Eu-Fe exchange and crystalline field. The use of the single-ion (molecular-field) approximation permits us to replace the Eu-Fe exchange interaction by an effective exchange field acting on the Eu3+ ions; the assumption is made that the anisotropy in the Eu-Fe exchange does not make a major contribution to the anisotropy of the ground state. We find that the isotropic exchange field and fourth-rank crystalline field first contribute to the cubic anisotropy of the ground state of Eu3+ in the fifth order of the energy; likewise the second-rank crystalline field contributes in the sixth order. The fifth- and sixth-order perturbation formulas for a Hermitian operator have been derived and are given in an Appendix. We calculate the anisotropy energy for a single Eu3+ ion in EuIG and average the results over the six magnetically inequivalent sites of the garnet structure. The order of magnitude of the calculated anisotropy constant K1 is in agreement with the experimental data that are available at low temperatures, but detailed comparison is not possible at present because of a relatively large number of poorly known parameters.