Since you did not provide a picture, I'm going to guess that the sensible question would be to find the remaining volume when the inner cylinder is removed or cut out from the bigger cylinder (blue region). That could be easily determined by subtracting the volume of the smaller cylinder to that of the bigger cylinder.
Volume of cylinder = π*r^2*h
Volume of shaded region = π*5^2*18 - π*2^2*18
Volume of shaded region = 378π = 1,187.52 cubic units