I think that the coefficient of cubical expansion of a substance depends on THE CHANGE IN VOLUME.
Cubical expansion, also known as, volumetric expansion has the following formula:
Δ V = β V₁ ΔT
V₁ = initial volume of the body
ΔT = change in temperature of the body
β = coefficient of volumetric expansion.
β is defined as the increase in volume per unit original volume per Kelvin rise in temperature.
With the above definition, it is safe to assume that the coefficient of cubical expansion of a substance depends on the change in volume, which also changes in response to the change in temperature.
