The unified-colored-noise approximation proposed by Jung and Hanggi is extended to the multi-dimensional case in this paper. Then, the Langevin equation and FokkerPlanck equation of colored cubic model for single mode dye-laser model are derived with this approximation method. The approximate formulas of the mean, variance, andskewness of the first-P8ssage-time distribution for the model are obtained and compared with the numerical simulations.