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Maintaining energy balance and economical operation is significant for multi-energy systems such as the energy hub. However, it is usually challenged by the frequently changing and unpredictable uncertainties at different timescales. Under this scope, this paper investigates the coordinated energy management problem for day-ahead and intra-day conditions considering uncertainties of source-load and market prices concurrently. Note that the precise knowledge of distributions about uncertainties may be unaccessible before the decision-making in day-ahead phase. A two-stage chance-constrained model based on distributionally robust approach with ambiguous moment information is proposed to immunize scheduling strategies against the worst-case probability distributions. The first stage is dedicated to obtaining more energy arbitrage and operation flexibility by optimizing bidding strategies in day-ahead power, natural gas and carbon markets. The second stage focuses on the optimization of worst-case expected operation cost. It provides a robust energy equipment and load scheduling strategy for the reference of subsequent intra-day arrangements. With respect to different variations of electrical and thermal components, an intra-day two-timescale coordination is implemented step by step. The energy scheduling is re-dispatched circularly to minimize the operation and penalty costs. The possible energy imbalance is also compensated by this way. As the energy management program is nonlinear, chance-constrained and multi-stage, linearization and dual transformation techniques are designed to enhance tractability of programs. Experimental results show that the developed multi-level framework results in a carbon emission decrease of 37%, and reduces energy cost averagely 3% compared with corresponding contrasting cases. The obtained strategy validates a good tradeoff between robustness and optimality.