The proliferation of network devices and novel bandwidth hungry applications over the existing network imposes novel challenges in terms of fulfilling the users' requirements. Dense deployment of small cells is thought to be a promising solution to fulfill these requirements. However, the user association in such dense networks becomes challenging and can greatly affect the network performance, as a user in such dense deployments can be connected to any of the available base stations. Traditionally, the user association has been performed based on the signal strength, however, such an approach does not apply when taking into account novel bandwidth hungry applications. Moreover, in recent years, a successful paradigm has been proposed to handle such bandwidth hungry applications, i.e., caching at small cell base stations. In this paper, we aim to solve this joint problem of user association and content caching in a dense small cell setting. To solve this problem, we present a novel iterative scheme that uses matching theory and a learning approach to find a suboptimal solution of the joint NP hard problem. Note that the user association and cache placement are strongly coupled, i.e., the association of users at a base station will determine the cache placement at base stations and the availability of cache at base stations will force the users to change their associations. Simulation results show that the proposed scheme (i.e., cache aware user association) significantly outperforms the cache unaware scheme and achieves a performance gain of up to 31% in terms of normalized utility and saves up to twice the backhaul bandwidth. Moreover, the proposed scheme also achieves up to 82% of the utility obtained by the optimal solution.