Proactively pushing content to users has emerged as a promising approach to improve the spectrum usage in off-peak times and reduce the peak data rate for fifth-generation (5G) mobile networks. However, owing to uncertainty of future user demands, base stations (BSs) may not receive payments for the pushed files. To motivate content pushing, economic incentives and user demand predictions become essential. Based on random content request delays of users, this paper studies the profit maximization for the BS and the spectrum provider (SP). Specifically, the SP sets different selling prices of bandwidth for pushing and on-demand services to enhance the spectrum usage and maximize its own profit. The BS, on the other hand, aims to maximize its profit by determining the amount of bandwidth purchased. The tension between the SP and the BS is formulated as a Stackelberg game. The single-user case is considered first to show the existence and uniqueness of a Stackelberg equilibrium (SE), and derive a closed-form expression for the SE. For the multiuser case, a distributed price updating algorithm is presented to obtain the SE. Numerical results show that the proposed game can achieve greater profit for both the SP and the BS, compared with the traditional on-demand system.