capacitor

outer has to be a shperical concentric shell not a sphere

no inner has to be a sphere:)

now it can be considered as a system of two capacitors as shown, first between the earthed sphere and shell and the second between shell and earth, that are clearly in parallel combination.

So C₁ = 4Πε₀abb - a (a general solution)

and C₂ = 4Πε₀b (for spherical conductor)

hence C_eff = C₁ + C₂

or C_eff = 4Πε₀b²b - a

this can also be proved by finding out the potential difference between the two...