The dynamic management of network resources is both a critical and challenging task in upcoming multi-tenant mobile networks, which requires allocating capacity to individual network slices so as to accommodate future time-varying service demands. Such an anticipatory resource configuration process must be driven by suitable predictors that take into account the monetary cost associated to overprovisioning or underprovisioning of networking capacity, computational power, memory, or storage. Legacy models that aim at forecasting traffic demands fail to capture these key economic aspects of network operation. To close this gap, we present DeepCog, a deep neural network architecture inspired by advances in image processing and trained via a dedicated loss function. Unlike traditional traffic volume predictors, DeepCog returns a cost-aware capacity forecast, which can be directly used by operators to take short-and long-term reallocation decisions that maximize their revenues. Extensive performance evaluations with real-world measurement data collected in a metropolitan-scale operational mobile network demonstrate the effectiveness of our proposed solution, which can reduce resource management costs by over 50% in practical case studies.