The Iterated Integral $\int_{0}^{\frac{\pi}{2}} \int_{0}^{\pi} \int_{0}^{2}e^{\rho^{3}} \rho^{2} d \rho d \theta d \varphi$

Multiple Choice

The iterated integral $\int_{0}^{\frac{\pi}{2}} \int_{0}^{\pi} \int_{0}^{2}e^{\rho^{3}} \rho^{2} d \rho d \theta d \varphi$ is

A) $\frac { \pi ^ { 2 } \left( e ^ { 8 } - 1 \right) } { 3 }$
B) $\frac { \pi ^ { 2 } \left( 1 - e ^ { - 8 } \right) } { 4 }$
C) $\frac { \pi ^ { 2 } \left( e ^ { 8 } - 1 \right) } { 5 }$
D) $\frac { \pi ^ { 2 } \left( e ^ { 8 } - 1 \right) } { 6 }$
E) $\frac { \pi ^ { 2 } \left( e ^ { 8 } - 1 \right) } { 7 }$