We give ab initio calculations for vacancies in Al. The calculations are based on the generalized-gradient approximation in the density-functional theory and employ the all-electron full-potential Korringa-Kohn-Rostoker Green's function method for point defects, which guarantees the correct embedding of the cluster of point defects in an otherwise perfect crystal. First, we confirm the recent calculated results of Carling [Phys. Rev. Lett. 85, 3862 (2000)], i.e., repulsion of the first-nearest-neighbor (1NN) divacancy in Al, and elucidate quantitatively the micromechanism of repulsion. Using the calculated results for vacancy formation energies and divacancy binding energies in Na, Mg, Al, and Si of face-centered-cubic, we show that the single vacancy in nearly free-electron systems becomes very stable with increasing free-electron density, due to the screening effect, and that the formation of divacancy destroys the stable electron distribution around the single vacancy, resulting in a repulsion of two vacancies on 1NN sites, so that the 1NN divacancy is unstable. Second, we show that the cluster expansion converges rapidly for the binding energies of vacancy agglomerates in Al. The binding energy of 13 vacancies consisting of a central vacancy and its 12 nearest neighbors, is reproduced within the error of 0.002 eV per vacancy, if many-body interaction energies up to the four-body terms are taken into account in the cluster expansion, being compared with the average error (>0.1 eV) of the glue models which are very often used to provide interatomic potentials for computer simulations. For the cluster expansion of the binding energies of impurities, we get the same convergence as that obtained for vacancies. Thus, the present cluster-expansion approach for the binding energies of agglomerates of vacancies and impurities in Al may provide accurate data to construct the interaction-parameter model for computer simulations which are strongly requested to study the dynamical process in the initial stage of the formation of the so-called Guinier-Preston zones of low-concentrated Al-based alloys such as Al(1-c)X(c) (X=Cu, Zn; c<0.05).