A procedure for synthesizing narrow size distribution cube-shaped Co₃O₄ nanoparticles ranging from 40 to 60 nm is reported. The rheological properties of suspensions of cubes in low molecular weight polyethylene glycol were studied over a wide range of particle volume fractions. At low volume fractions these suspensions display Newtonian fluid behavior, while at high volume fractions they manifest complex rheological characteristics, including shear thinning, shear thickening and a yield stress. Pronounced shear thinning was observed at particle volume fractions Φ as low as 0.14, and shear thickening observed at Φ ≈ 0.36.  For particle volume fractions ranging from 0.36-0.62, the onset of shear thickening is found to occur at increasingly lower shear rates, reaching a minimum of 40s^-1 at Φ  = 0.62. These findings are discussed through comparisons to suspensions of spherical particles and models designed to predict the relative viscosity and shear thickening transition in colloidal suspensions.