The purpose of this paper is to present the Monte Carlo (MC) method augmented by the B1 spectrum to generate few-group diffusion theory constants, to assess their qualification in terms of the core depletion analysis, and thus to validate the MC method implemented into the Seoul National University MC code, McCARD, as a few-group diffusion theory constant generator. To do so, two-step core neutronics analyses are conducted for two types of power reactors, pressurized water reactors and very high temperature gas-cooled reactors, by the McCARD/MASTER code system in which McCARD is used as a MC few-group constant generation code and MASTER as a deterministic core analysis code. The two-step calculations for the effective multiplication factors and assembly power distributions of the two types of power reactor cores by McCARD/MASTER are compared with the reference calculations from McCARD, the nuclear design report, or measurements. By showing excellent agreement between McCARD/MASTER and the reference neutronics analyses for the two types of power reactors, it is concluded that the MC method implemented in McCARD can generate few-group diffusion theory constants that are well qualified for high-accuracy two-step core neutronics calculations.