I found this question What is the usage of CYK algorithm in the real world considering we have algorithms with a much better Time complexity? saying CYK Parsing algorithm can compute any Context Free Grammar in $O(n^3)$.
But this does not make sense because I cannot see how NonDeterministic Context Free grammar can be parsed in $O(n^3)$. Then, while reading Hopcroft and Ullman (2006) pages 304 I found:
In $O(n^3)$ time the algorithm constructs a table that tells whether w is in L $\in$ Note that when computing this running time the grammar itself is considered fixed and its size contributes only a constant factor to the running time which is measured in terms of the length of the string w whose membership in L is being tested.
So, the correct affirmation is: There is no way a NonDeterministic Context Free Grammar parsing tree can be built in $O(n^3)$ time, only its word membership can be determined in $O(n^3)$ time by the CYK algorithm. NonDeterministic Context-Free Grammars Parsing Trees can only be built in Exponential Time (worst case)?