  The 1/8 BPS $D^6\mathcal{R}^4$ coupling in type II string theory compactified
on $T^2$ receives contributions from worldsheet instantons and anti-instantons
wrapping the $T^2$, up to genus three in string perturbation theory. These
involve contributions separately from bound states of instantons and
anti-instantons, which are qualitatively similar to such contributions to the
1/2 and 1/4 BPS couplings. At genus two, the $D^6\mathcal{R}^4$ coupling also
receives contributions from instanton/anti-instanton bound states unlike the
1/2 and 1/4 BPS couplings, which is a consequence of a T-duality invariant
eigenvalue equation a term in the coupling satisfies. We solve this eigenvalue
equation to obtain the complete structure of the worldsheet (anti)instanton
contributions. In the type IIB theory, strong weak coupling duality leads to
certain contributions involving bound states of D string (anti)instantons
wrapping the $T^2$.
