We study degraded broadcast channels (BCs) with caching receivers and show that caching offers new global caching gains that can be achieved by smart cache assignment and joint cache-channel coding. We define the global capacity-memory tradeoff as the largest capacity-memory tradeoff that can be attained by optimizing the receivers cache-assignment subject to a total cache memory budget, and establish lower and upper bounds on it. The bounds coincide when the total cache memory budget is sufficiently small or sufficiently large, characterized in terms of the BC statistics. The lower bound is achieved by piggyback coding, superposition coding, and generalizing the coded caching of Maddah-Ali and Niesen. The upper bound is established by providing each user with the content of weaker users' cache memories. When the BC is a common noise-free bit-pipe, the upper bound on the rate leads to a lower bound on the delivery rate and characterizes the optimal delivery rate within a multiplicative gap of 2.35 for any number of users.