Given $n$ and $k$ two positive integers we begin with an urn that contains $kn$ white balls. We then proceed through $n$ turns where on each turn $k$ black balls are added to the urn and then $2k$ random balls are removed from the urn.

We let $B_t(n,k)$ be the number of black balls that are removed on turn $t$.

Further define $E(n,k)$ as the expectation of ${\displaystyle \sum _{t=1}^n{B}_t(n,k{)}^2}$.

You are given $E(2,2)=9.6$.

Find $E({10}^6,10)$. Round your answer to the nearest whole number.