The cubic model, described by the Hamiltonian ⋅=−J&Sgr;<ij≳ &sgr;i&sgr;j&dgr;&agr;i&dgr;&agr;jwhere &sgr;i=±1 and &agr;i=x, y, or z, is subjected to a Monte Carlo simulation. For an 8×8×8 fcc lattice, it is found that the system exhibits a first order transition at kBTo/J=3.45±0.01 in fairly close agreement with results obtained previously by the Kikuchi approximation. Discontinuities at the phase transition and stability limits for the metastable states on either side of the phase transition are also investigated.