y is inversely proportional to the cube of x
means y is inversely proportional to x³

so y = k/x³, k is a constant

y = 128 for certain value of x.

128 = k/x³

So when x is doubled, it becomes 2x.

So just sub 2x instead of x.

So k/(2x)³ = k/(2³ × x³)
= k/(8x³)
= ⅛ × k/x³
= ⅛ × 128 (from above)

So, y becomes ⅛ of it's original value when x is doubled.

Value of y = ⅛ × 128 = 16

Another way to see it is :

When x is double of the original value (×2),
x³ → (×2)³ → ×8 of the original value.

So since y is inversely proportional to x³,

y→ × ⅛ of the original value.

So 128 x ⅛ = 16