Efficient and effective system-level power management for multi-core systems with multiple voltage islands is necessary for next-generation computing systems. This paper considers energy efficiency for such systems, in which the cores in the same voltage island have to be operated at the same supply voltage level. We explore how to map given task sets onto cores, so that each task set is assigned and executed on one core and the energy consumption is minimized. Due to the restriction to operate at the same supply voltage in a voltage island, different mappings will result in different energy consumptions. By using the simple Single Frequency Approximation Scheme (SFA) to decide the voltages and frequencies of individual voltage islands, this paper presents the approximation factor analysis (in terms of energy consumption) for simple heuristic algorithms, and develops a dynamic programming algorithm, which derives optimal mapping solutions for energy minimization when using SFA. We experimentally evaluate the running time and energy consumption performance of these algorithms on Intel's Single-chip Cloud Computer (SCC). Moreover, we conduct simulations for hypothetical platforms with different number of voltage islands and cores per island, also considering different task partitioning policies.