Answer
$$6.85202$$
Work Step by Step
$$\eqalign{
& \int_0^2 {\int_x^2 {\sqrt {16 - {x^3} - {y^3}} } dy} dx \cr
& {\text{Using a computer algebra system to evaluate the }} \cr
& {\text{iterated integral, we obtain:}}{\text{}} \cr
& \int_0^2 {\int_x^2 {\sqrt {16 - {x^3} - {y^3}} } dy} dx \approx 6.85202 \cr} $$
