Borel-Weil-Bott theorem vs the usual formula

Question

I am confused about the Borel-Weil-Bott theorem.

For example, if I try to compute $H^i(\mathbb{P}^5,\mathcal{O}(-8)),$ Borel-Weil-Bott computation is the following:

1. Find the sequence: $\sigma= (0,0,0,0,0,8)+(6,5,4,3,2,1)=(6,5,4,3,2,9)$
2. There are no repetitions, so not all cohomologies are zero.
3. There are 5 'disarrangements', that is, in this sequence there are 5 pairs of numbers that are not decreasing.
4. We should sort $\sigma$: $\tilde{\sigma}=(9,6,5,4,3,2)$ and subtract $(6,5,4,3,2,1)$, the result is $(3,1,1,1,1,1).$
5. Finally, the answer is $H^5(\mathbb{P}^5,\mathcal{O}(-8))=W_{(3,1,1,1,1,1)}.$

But we know that $H^5(\mathbb{P}^5,\mathcal{O}(-8))=Sym^2(V)=W_{(2,0,0,0,0,0)}.$

I don't understand why the results are different.