Most data generated by modern applications is stored in the cloud, and there is an exponential growth in the volume of jobs to access these data and perform computations using them. The volume of data access or computing jobs can be heterogeneous across different job types and can unpredictably change over time. Cloud service providers cope with this demand heterogeneity and unpredictability by over-provisioning the number of servers hosting each job type. In this paper, we propose the addition of erasure-coded servers that can flexibly serve multiple job types without additional storage cost. We analyze the service capacity region and the response time of such erasure-coded systems and compare them with standard uncoded replication-based systems currently used in the cloud. We show that coding expands the service capacity region, thus enabling the system to handle variability in demand for different data types. Moreover, we characterize the response time of the coded system in various arrival rate regimes. This analysis reveals that adding even a small number of coded servers can significantly reduce the mean response time, with a drastic reduction in regimes where the demand is skewed across different job types.