To better understand the energetics of hydrophobic core formation in protein folding under ambient conditions, the potential of mean force (PMF) for different three-methane configurations in an aqueous environment is computed by constant-pressure Monte Carlo sampling using the TIP4P model of water at 25 degreesC under atmospheric pressure. Whether the hydrophobic interaction is additive, cooperative or anti-cooperative is determined by whether the directly simulated three-methane PMF is equal to, more favorable, or less favorable than the sum of two-methane PMFs. To ensure that comparisons between PMFs are physically meaningful, a test-particle insertion technique is employed to provide unequivocal correspondence between zero PMF value and the nonexistent inter-methane interaction (zero reference-state free energy) experienced by a pair of methanes infinitely far apart. Substantial deviations from pairwise additivity are observed. Significantly, a majority of the three-methane configurations investigated exhibit anti-cooperativity. Previously simulated three-methane PMFs were defined along only one single coordinate. In contrast, our technique enables efficient computation of a three-methane PMF that depends on two independent position variables. The new results show that the magnitude and sign of nonadditivity exhibit a prominent angular dependence, highlighting the complexity of multiple-body hydrophobic interactions. Packing consideration of crystal-like constructs of an infinite number of methanes and analysis of methane sublimation and hydration data suggest that anti-cooperativity may be a prevalent feature in hydrophobic interactions. Ramifications for protein folding are discussed.