This paper proposes M3-Net, a cost-effective, graph-free multilayer perceptron (MLP)-based model for accurate traffic volume prediction, essential for the development of intelligent transportation systems. Existing deep learning-based traffic volume prediction models either rely on the complete transportation network structure or require complex model designs to capture complex spatiotemporal dependencies. M3-Net addresses these issues by utilizing time-series and spatiotemporal embeddings for efficient feature processing and introducing a novel MLP-Mixer architecture with a Mixture of Experts (MoE) mechanism. Experiments on various real-world datasets demonstrate the superior predictive performance and lightweight deployability of the proposed model.