I plotted a sketch of y = x3, y = 8 and x = 1 and shaded the region R.
The region shaded orange is the region you need to revolve around the y-axis. Either the disk or shell method will work but I think in this situation the cylindrical shell method results in an easier integral.
To use the cylindrical shell method take a vertical slice through the region R of thickness x and revolve this slice around the y-axis.
Is this enough help? Let us know.