\( \begin{array}{ll}x^{3} & \text { (6) } \\ \text { (9) } b^{3}-216 & 5 x^{3}+40 \\ \text { (8) }-x^{3}-27 & 343-(a-1)^{3}\end{array} \)

The expression you've presented looks like a set of polynomial equations or terms that revolve around cubes, particularly \( x^{3} \), \( b^{3} \), and expressions like \( (a-1)^{3} \). A fun fact about cubic expressions is that they can often be factored using identities like the sum and difference of cubes! For instance, \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \) and \( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \). This can be particularly helpful when calculating or simplifying these types of expressions. When dealing with cubic expressions, one common mistake is forgetting to simplify fully or overlooking signs when applying the cube formulas. Additionally, ensure you check for possible factoring; often, terms may appear independently when they can be combined nicely through factoring. A good approach is to always look for common terms and apply polynomial long division if necessary! Remember, a clear workspace and methodical approach can save loads of confusion.