General term of $\left(2 x^{2}-\frac{1}{x}\right)^{8}$ is

$^{8} \mathrm{C}_{\mathrm{r}}\left(2 \mathrm{x}^{2}\right)^{8-\mathrm{r}}\left(\frac{-1}{\mathrm{x}}\right)^{\mathrm{r}}$

$\therefore $ Given expression is equal to

$\left(1-\frac{1}{x}+3 x^{5}\right)^{8} C_{r}\left(2 x^{2}\right)^{8-\tau}\left(-\frac{1}{x}\right)^{r}$

${ = ^8}{{\text{C}}_{\text{r}}}{\left( {2{{\text{x}}^2}} \right)^{8 – {\text{r}}}}{\left( { – \frac{1}{{\text{x}}}} \right)^{\text{r}}} – {\frac{1}{{\text{x}}}^8}{{\text{C}}_{\text{r}}}{\left( {2{{\text{x}}^2}} \right)^{8 – {\text{r}}}}{\left( { – \frac{1}{{\text{x}}}} \right)^r}$

$ + 3{{\text{x}}^5}{ \cdot ^8}{{\text{C}}_{\text{r}}}{\left( {2{{\text{x}}^2}} \right)^{8 – {\text{r}}}}{\left( { – \frac{1}{{\text{x}}}} \right)^{\text{r}}}$

${ = ^8}{{\text{C}}_{\text{T}}}{2^{8 – {\text{r}}}}{( – 1)^{\text{r}}}{{\text{x}}^{16 – 3{\text{r}}}}{ – ^8}{{\text{C}}_{\text{r}}}{2^{8 – {\text{r}}}}{( – 1)^{\text{r}}}{{\text{x}}^{15 – 3{\text{r}}}}$

$ + 3{ \cdot ^8}{{\text{C}}_{\text{r}}}{2^{(8 – {\text{r}})}}{\left( { – \frac{1}{{\text{x}}}} \right)^{\text{r}}}{( – 1)^{\text{r}}}{{\text{x}}^{21 – 3{\text{r}}}}$

For the term independent of $x,$ we should have

$16-3 r=0,15-3 r=0,21-3 r=0$

From the simplification we get $r=5$ and $r=7$

$\therefore-^{8} C_{5}\left(2^{3}\right)(-1)^{5}-3 \cdot^{8} C_{7} \cdot 2$

$+\left[\frac{8 !}{5 ! 3 !} \times 8\right]-3 \times\left[\frac{8 !}{7 ! 1 !} \times 2\right]$

$=(56\times 8)-48$

$=448-6\times 8=448-48=400$