If for some α, β; α ≤ β, α+β=8 and sec^2( tan^-1 α)+ cosec^2( cot^-1 β)=36, then α^2+β is ____.

If for some $\displaystyle \alpha, \beta ; \alpha \leq \beta, \alpha+\beta=8$ and $\displaystyle \sec ^2\left(\tan ^{-1} \alpha\right)+\operatorname{cosec}^2\left(\cot ^{-1} \beta\right)=36$, then $\displaystyle \alpha^2+\beta$ is $\displaystyle \_\_\_\_$.