In the field of intelligent mining, simultaneous localization and mapping (SLAM) is a crucial technology that contributes to the development of unmanned mining operations. This paper presents a robust cubature Kalman filtering algorithm for SLAM applications for scenarios where the measurement noise exhibits colored heavy-tailed features. First, the colored measurement noise is eliminated by the measurement differencing method. Then, within the variational Bayesian framework, we model the heavy-tailed noise using the generalized hyperbolic distribution. Through a series of iterative processes, we obtain the posterior distribution of the system state vector, the noise covariance matrix, and the auxiliary parameter. The generalized hyperbolic distribution can degenerate into a variety of heavy-tailed distributions, and thus our proposed algorithm is a framework for solving the state estimation problem under colored heavy-tailed measurement noise. Through a comprehensive approach that includes 2D target tracking simulation, SLAM environment simulation, and experiments on real datasets, we perform a comparative analysis between the proposed algorithm and existing algorithms. Our results demonstrate the superior estimation capability of the proposed algorithm.