Summary: ``This paper explores multimode function multistability of Cohen-Grossberg neural networks (CGNNs) with Gaussian activation functions and mixed time delays. We start by using the geometrical properties of Gaussian functions. The state space is partitioned into $3^\mu$ subspaces, where $0 \leq\mu\leq n$. Moreover, through the utilization of Brouwer's fixed point theorem and contraction mapping, some sufficient conditions are acquired to ensure the existence of precisely $3^\mu$ equilibria for $n$-dimensional CGNNs. Meanwhile, there are $2^\mu$ and $3^\mu - 2^\mu$ multimode function stable and unstable equilibrium points, respectively. Ultimately, two illustrative examples are provided to confirm the efficacy of theoretical results.''