These are the first four diagrams of a sequence. The diagrams are made from white dots and black dots. $$\(T\)$$ is the total number of dots used to make all of the first $$\(n\)$$ diagrams. $$\[ T=a n^{3}+b n^{2} \]$$ Find the value of $$\(a\)$$ and the value of $$\(b\)$$. You must show all your working. $$\[ \begin{aligned} & a= ............................................ \\ & b= ............................................ \end{aligned} \]$$

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