Volume of solids

$\text{area of yellow region}=3(2)(2)=12$

$\text{area of green region}=2(4)(12)=96$

$\text{area of blue region}=5(2)(2)=20$

$\text{area of red region}=2(2)(4)=16$

$\text{area of gray region}=5(2)(2)=20$

$\text{area of brown region}=4(4)=16$

$\text{area of violet region}=4(8)=32$

$\text{cross-section area}=12+96+20+16+20+16+32=212$

Therefore, the volume is $212(2)=\color{#D61F06}\boxed{424}$