If U is inversely proportional to the cube of V, then we can write the relationship between U and V as UV\(^3\) = k, where k is the constant of proportionality. We can find the value of k by using the information that U = 81 when V = 2:

\(81 \times 2^3 = k\)

\(k = 648\)

Now that we know the value of k, we can use it to find the value of U when V = 3:

\(UV^3 = 648\)

\(U \times 3^3 = 648\)

\(U = \frac{648}{27}\)

\(U = 24\)

So, when V = 3, U is equal to 24.