(2/9n + 9/2m)^3 = (2/9n + 9/2m)(2/9n + 9/2m)(2/9n + 9/2m)
= (4/81n^2 + 4/9mn + 81/4m^2)(2/9n + 9/2m)
= 8/243n^3 + 80/27n^2m + 729/8nm^2 + 162/27n^2m + 1620/9mn^2 + 3645/2m^3
= 8/243n^3 + 242/27n^2m + 729/4nm^2 + 405/2m^3.
(2/9n + 9/2m)^3 = (2/9n + 9/2m)(2/9n + 9/2m)(2/9n + 9/2m)
= (4/81n^2 + 4/9mn + 81/4m^2)(2/9n + 9/2m)
= 8/243n^3 + 80/27n^2m + 729/8nm^2 + 162/27n^2m + 1620/9mn^2 + 3645/2m^3
= 8/243n^3 + 242/27n^2m + 729/4nm^2 + 405/2m^3.