The N_f^3 g^6 term in the pressure of hot QCD

We determine the first independent part of the g^6 coefficient in the weak coupling expansion of the QCD pressure at high temperatures, the one proportional to the maximal power of the number of quark flavors N_f. In addition to introducing and developing computational methods that can be used in evaluating other parts of the expansion, our calculation provides a result that becomes dominant in the limit of large N_f and a fixed effective coupling g_{eff}^2 = g^2 N_f/2.