It is given that z varies directly with y and directly with the cube of x.
[tex]z=kyx^3[/tex]Where k is the constant of proportionality.
First, we need to find the value of k.
It is given that z = 2560 when x = 4 and y = 10
[tex]\begin{gathered} z=kyx^3 \\ \frac{z}{yx^3}=k \\ k=\frac{z}{yx^3} \\ k=\frac{2560}{10\cdot(4)^3} \\ k=4 \end{gathered}[/tex]So, the value of k is 4
The relation becomes
[tex]z=4yx^3[/tex]Now we can easily find the value of z when x = 8 and y = 4
[tex]\begin{gathered} z=4(4)(8)^3 \\ z=4(4)(512) \\ z=8192 \end{gathered}[/tex]Therefore, the value of z is 8192
