Topological optimization is a powerful tool for maximizing structural performance, en abling multifunctionality of the structure, and reducing the materials waste and cost for sustainable manufacturing. However, current topology optimization tools are limited to a few scales, and the potential of the nested topology optimization in engineering design has yet to be realized. I proposed a mechanistic design theory to introduce nested scales [n], design regions [d], and the material design [m] in large-scale topology design for multifunctional performance. To implement this concurrent nested topology design theory, a new mechanistic reduced-order method is developed by combining the higher-order accurate Convolution Hierarchical Deep Learning (C-HiDeNN) with computationally efficient Tensor Decomposition (TD) techniques. The built-in convolution filter in C-HiDeNN-TD method enables higher-order accuracy, arbitrary smoothness, and length-scale control to avoid checkerboard patterns without adding extra degrees of freedoms which are some well-known challenges in topology optimization problems. The C-HiDeNN-TD-TO enables solution of high-resolution TO problems (billions of degrees of freedoms in finite element) in a single scale to nested n-scales, leveraging the concurrent application of nested topology design theory. I demonstrate the effectiveness of this approach through examples such as a bamboo-like structure for nested lattice structures (up to 12 scales) and different design regions with materials selection, resulting in improved multifunctional performance under axial, bending, and torsional forces. The proposed design theory enables fractal and beyond fractal designs at the lattice level, promoting structural stability with functional gradient designs observed in natural structures. Similarly, nested lattice design and materials selection lead to improved performance in a drone and car bumper structure. The materials design opportunity of the proposed theory is discussed, and the material design aspects in design of a non-linear cantilever beam is demonstrated using clustering-based machine learning approach. The mechanics nested lattice design theory has the potential for multifunctional multiphysics nested lattice design such as the acoustic meta material, robotic material, thermal conductivity meta material. It also opens an avenue in efficient engineering structures, cost-effective product design and fosters innovation in manufacturing technology.