\[\boxed{\mathbf{4.174}}\]
\[V_{A} = 2 \cdot 4 \cdot 1 = 8\ \left( мм^{3} \right).\]
\[V_{B} = 3 \cdot 3 \cdot 2 = 18\ \left( мм^{3} \right).\]
\[V_{C} = 10 \cdot 10 \cdot 10 - 2 =\]
\[= 1000 - 2 = 998\ \left( мм^{3} \right).\]
\[V_{D} = 10 \cdot 10 \cdot 1 = 100\ \left( мм^{3} \right).\]
\[V_{E} = 10 \cdot 10 \cdot 7 - 1 \cdot 1 \cdot 7 =\]
\[= 700 - 7 = 693\ \left( мм^{3} \right).\]