Given that \(T\) varies inversely as the cube of \(R\), we can express this relationship as:

\[T = \frac{k}{R^3}\]

where \(k\) is the constant of variation.

We are given that when \(R = 3\) and \(T = \frac{2}{81}\), we can substitute these values into the equation to find \(k\):

\[\frac{2}{81} = \frac{k}{3^3}\]

\[\frac{2}{81} = \frac{k}{27}\]

\[k = \frac{2 \cdot 27}{81}\]

\[k = \frac{54}{81}\]

\[k = \frac{2}{3}\]

Now that we have the constant of variation \(k = \frac{2}{3}\), we can use it to find \(T\) when \(R = 2\):

\[T = \frac{\frac{2}{3}}{2^3}\]

\[T = \frac{\frac{2}{3}}{8}\]

\[T = \frac{2}{3} \cdot \frac{1}{8}\]

\[T = \frac{1}{12}\]

So, when \(R = 2\), \(T = \frac{1}{12}\).