In this paper, we consider a multi-cell multi-band downlink where the base-station (BS) in each cell has multiple transmit antennas and each cell has one active mobile station (MS) with a single receive antenna and treats interference from the other cells as noise. There is a sum transmit power constraint for each BS over all the bands. An alternating maximization (AM) algorithm is proposed to determine the optimal power allocation among the bands and the optimal beamforming vectors for each BS in each band. This algorithm can be implemented in a distributed manner with limited exchange of interference constraints between the BSs. Using simulations, the algorithm is shown to converge to the weighted sum rate optimal point on the Pareto boundary of the achievable rate region. Furthermore, significant performance gain is observed compared to: (i) equal power allocation across bands and weighted sum rate optimization in each band, (ii) zero-forcing (ZF) beamforming, and (iii) maximal ratio transmission (MRT) beamforming.