Prefixes of the Fibonacci word that end with a cube

The Fibonacci word f=010010100100101⋯ is one of the most well-studied words in area combinatorics on words. It not periodic, but nevertheless contains many highly periodic factors (contiguous subwords). For example, it cubes (i.e., non-empty form xxx). We study prefixes that end with a cube. Using computer prover Walnut, we obtain an exact description positions at which cube ends. This gives certain measure how close to being periodic.