Cumulative distribution function (CDF)-based scheduling (CS) has been known as an efficient technique for cellular networks, which satisfies arbitrary channel access ratio requirements of users in a cell, while efficiently exploiting multiuser diversity (MUD). In this paper, we mathematically analyze both throughput and energy efficiency (EE) of CS in a multi-cell downlink network where the users are non-uniformly distributed in each hexagonal cell. We assume that the number of users are generated according to Poisson point process (PPP) in each cell, and thus the number of users may change for each cell. If there exists no user in a particular cell, then the base station (BS) of the cell is assumed to be turned-off for improving EE. In the multi-cell network, each BS with CS selects the user having the largest CDF value of the received signal-to-interference-plus-noise ratio (SINR). We show that both throughput and EE of CS in the multi-cell network increase as the user density increases and they also increase as users tend to exist nearer to the BS. CS obviously outperforms the round-robin (RR) scheduling in terms of both throughput and EE. The analysis is validated with extensive computer simulations. To the best of our knowledge, the mathematical analysis of the CS in the multi-cell network with non-uniform user distribution has not been provided so far.