\[\boxed{\mathbf{242}.}\]
\[1)\ 16^{3} + 31^{4} - 2 = (15 + 1)^{3} +\]
\[+ (30 + 1)^{4} - 2 =\]
\[= 15^{3} + 3 \cdot 15^{2} + 3 \cdot 15 + 1 +\]
\[+ 30^{4} + 4 \cdot 30^{3} + 6 \cdot 30^{2} +\]
\[+ 4 \cdot 30 + 1 - 2 =\]