Optimal capacity configuration (OCC) of large-scale energy bases with multi-timescale operation characteristics presents a critical challenge. To address the problem, this study proposes an OCC approach of large-scale energy bases considering external multi-stochastic scenarios and interactive multi-timescale objectives. Firstly, guided by the system theory, the nonlinear state-space description is presented for systematic analysis of a general large-scale energy base. Due to interactive multi-timescale objectives between annual and daily cumulative objectives, a nested optimization structure is established. Then, considering the external multi-stochastic scenarios caused by the variables such as wind speed, solar irradiance, electric load, and thermal load, a multi-step optimization strategy is proposed including pre-configuration in regular scenarios and re-configuration by introducing micro-incremental scenarios. The multi-step optimization strategy and nested optimization structure jointly achieve the OCC of the large-scale energy base. In each step, the nested optimization structure is executed once. Finally, while ensuring the balance between thermal supply and load demand, the imbalances between electric power supply and the load demand are eliminated, significantly showing the efficiency of the proposed OCC approach.