7．
\((1)(2x-3)^{5}\)展开式中\(x^{3}\)的系数为________．
\((2)\)已知正方体\(ABCD—A_{1}B_{1}C_{1}D_{1}\)的八个顶点郁在半径为\(\sqrt{3}\)的球面上\(.\)则此正方体的体积为________．
\((3)\)若\(x\)，\(y\)满足约束条件\(\begin{cases} & x-y+1\leqslant 0, \\ & x-2y\leqslant 0, \\ & x+2y-2\leqslant 0, \end{cases}\)则\(z=x+y\)的最大值是________．
\((4)\)若数列\(\{\dfrac{{{a}_{n}}}{n}+1\}\)是公比为\(2\)的等比数列，且\(a_{1}=1\)，则\(\{a_{n}\}\)的前\(n\)项和\(S_{n}=\)________．