An analytical study of free convection in a cubic cavity of fluid-saturated porous material is reported. The analytical algorithm integrates the Darcy-Boussinesq equations formulated in terms of pressure and temperature. The dependent variables (P, T) are expressed using an asymptotic development in the parameter ξ = (Ra - Rac)1/2/π where Rac = 4 π2 denotes the value of the critical Rayleigh number, in a cubic cavity (Rac1 = 4 π2 for the 2D flow and Rac2 = 4.5 π2 for 3D flow). Terms up to order 48 for the 2D flow and up to order 16 for the 3D flow are computed. The analytical value of the Nusselt number is in good agreement with a numerical one obtained using a Legendre spectral collocation method.