Middle term in the expansion of ${\left(1-3\mathrm{x}+3{\mathrm{x}}^2-{\mathrm{x}}^3\right)}^{2\mathrm{n}}$ is

${\left(1-3\mathrm{x}+3{\mathrm{x}}^2-{\mathrm{x}}^3\right)}^{2\mathrm{n}}={\left({\left(1-x\right)}^3\right)}^{2n}=(1-\mathrm{x}{)}^{6\mathrm{n}}\text{, Middle term is }{\mathrm{T}}_{3n+1}$

$T_{3n+1}={ }^{6n}{C}_{3n}{\left(-x\right)}^{3n}\Rightarrow T_{3n+1}=\frac{\left(6\mathrm{n}\right)!}{\left(3\mathrm{n}\right)! \left(3\mathrm{n}\right)!}(-\mathrm{x}{)}^{3\mathrm{n}}$