(2) \( x^{3}-\frac{1}{x^{3}} \)

The expression \( x^{3} - \frac{1}{x^{3}} \) can be related to the cubic identities. Specifically, it can be derived from the formula for \( a^3 - b^3 \), which factors as \( (a-b)(a^2 + ab + b^2) \). In this case, letting \( a = x \) and \( b = \frac{1}{x} \) opens up interesting paths to explore its properties, such as its value at certain key points. In practical applications, expressions like \( x^{3} - \frac{1}{x^{3}} \) often occur in physics and engineering, especially in contexts involving cubic variables and inverses. For example, it appears in calculations involving rotational dynamics or fluid dynamics when working with moment of inertia or flow rates, where cubic relationships describe the behavior of physical systems.