Tutorial: https://en.algorithmica.org/hpc/algorithms/matmul/

A version you can submit on CodeForces (it is optimized for a specific CPU that is very different from that of CF, so the speedup is smaller): https://github.com/sslotin/amh-code/blob/main/matmul/self-contained.cc

These blocking/vectorization techniques can also be applied to some dynamic programming algorithms, such as the Floyd-Warshall ("for-for-for") algorithm. Do you know any similar DP problems where the number of operations is larger than the number of states?