Efficient power management in smart grids requires obtaining power consumption data from each resident. However, data concerning user's electricity consumption might reveal sensitive information, such as living habits and lifestyles. In order to solve this problem, this paper proposes a privacy-preserving cube-data aggregation scheme for electricity consumption. In our scheme, a data item is described as a multi-dimensional data structure (l-dimensional), and users form and live in multiple residential areas (m areas, and at most n users in each area). Based on Horner's Rule, for each user, we construct a user-level polynomial to store dimensional values in a single data space by using the first Horner parameter. After embedding the second Horner parameter into the polynomial, the polynomial is hidden by using Paillier cryptosystem. By aggregating data from m areas, we hide the area-level polynomial into the final output. Moreover, we propose a batch verification scheme in multi-dimensional data to reduce authentication cost. Finally, our analysis shows that the proposed scheme is efficient in terms of computation and communication costs, suitable for massive user groups, and supports the flexible and rapid growth of residential scales in smart grids.