From Gauss's law, Electric field outside the ball will not depend on the internal charge distribution it will depend only on the Total charge, so using integration we would first calculate the total charge of the solid ball

the total charge of the solid ball= 2 π ρ(not)R^3

therefore electric field outside the solid ball will be similar to the electric field generated by a point charge of magnitude 2 π ρ(not)R^3