We consider a multidimensional cosmological model with FRW typemetric having 4-dimensional space-time and d-dimensionalRicci-flat internal space sectors with a higher dimensionalcosmological constant. We study the classical cosmology incommutative and GUP cases and obtain the corresponding exactsolutions for negative and positive cosmological constants. It isshown that for negative cosmological constant, the commutative andGUP cases result in finite size universes with smaller size andlonger ages, and larger size and shorter age, respectively. Forpositive cosmological constant, the commutative and GUP casesresult in infinite size universes having late time acceleratingbehavior in good agreement with current observations. Theaccelerating phase starts in the GUP case sooner than thecommutative case. In both commutative and GUP cases, and for bothnegative and positive cosmological constants, the internal spaceis stabilized to the sub-Planck size, at least within the presentage of the universe. Then, we study the quantum cosmology byderiving the Wheeler-DeWitt equation, and obtain the exactsolutions in the commutative case and the perturbative solutionsin GUP case, to first order in the GUP small parameter, for bothnegative and positive cosmological constants. It is shown thatgood correspondence exists between the classical and quantumsolutions.