Evaluate the iterated integral.

${\displaystyle \underset{0}{\overset{2}{}}}{\displaystyle \underset{0}{\overset{y}{}}}{\displaystyle \underset{0}{\overset{x}{}}}8cos(x+y+z)dzdxdy$

Step $1$

We start with the innermost integral. When integrating with respect to $z,$ the other variables $x$ and $y$ are considered constants, and so

Step $2$

Next, integrating with respect to $x$ means that $y$ is constant, and so