After constructing the recursion tree i concluded a cost of $n^2\cdot log_2(n)-i\cdot n^2$ per level. So my total cost is:
$$\sum_{i=0}^{log_2(n)}n^2\cdot log_2(n)-i\cdot n^2$$
$$=(log_2(n)+1)\cdot n^2\cdot log_2(n)-\sum_{i=0}^{log_2(n)}i\cdot n^2$$ $$=n^2\cdot log_2^2(n)+n^2\cdot log_2(n)-\sum_{i=0}^{log_2(n)}i\cdot n^2$$
Because $n^2\cdot log_2(n)$ and $\sum_{i=0}^{log_2(n)}i\cdot n^2$ are lower order terms i concluded $T(n) \in \Theta (n^2\cdot log_2^2(n))$
I would appreciate if someone could tell me wether i'm wrong or right.
