If $X$ is a smooth projective variety over a field, $Z\subset X$ a smooth closed subvariety of codimension $d$, $X'\to X$ the blowup of $X$ along $Z$, there's the blowup formula

$$H^j(X'_{et},\mathbf{Z}(n)) = H^j(X_{et},\mathbf{Z}(n))\oplus\bigoplus_{r=1}^{d-1}H^{j-2r}(Z_{et},\mathbf{Z}(j-r)).$$

I must be missing something. For $j = 2n+1$ and $n = 1$, we get

$$Br(X') = Br(X) \oplus(things)$$

and it isn't clear to me the "things" vanish. But we know the cohomological Brauer group is a birational invariant of $X$, so they must vanish.

What do I not know about $H^{j-2r}(Z_{et},\mathbf{Z}(j-r))$?