The degraded K-receiver broadcast channel (BC) is studied when receivers are aided with cache memories. Lower and upper bounds are derived on the capacity-memory tradeoff, i.e., on the largest rate that can be achieved as a function of the receivers' cache sizes. The lower bounds are achieved by two new coding schemes that benefit from non-uniform cache assignment. The paper also provides lower and upper bounds on the global capacity-memory tradeoff of degraded BCs, i.e., on the largest capacity-memory tradeoff that can be attained by optimizing the receivers cache-assignment subject to a total cache memory budget. The bounds coincide when the total cache memory budget is sufficiently small or sufficiently large, with the thresholds depending on the BC statistics. For a small total cache budget M, it is optimal to assign all the cache memory to the weakest receiver. In this regime, the global capacity-memory tradeoff grows as M/D, where D denotes the total number of files in the system. For a large total cache budget, it is optimal to assign a positive cache memory to every receiver, where weaker receivers are assigned larger cache memories than stronger receivers. When the total cache budget M exceeds a threshold, then the global capacity-memory tradeoff grows as 1/K.M/D.A uniform cache-assignment policy is suboptimal.