Yes; heat capacity, in units of "J/"^@ "C"J/∘C, or "J/K"J/K, is an extensive property, and does scale with volume. This is why you should watch your units.
On the other hand, specific heat capacity, sometimes given as c_scs, in units of "J/g"^@ "C"J/g∘C or "J/g"cdot"K"J/g⋅K, is an intensive property, completely independent of the amount of substance, and depends only on its identity.
It is often seen in the equation for heat flow through a substance that causes a temperature change:
q = overbrace(m underbrace(c_s)_"Specific Heat Capacity")^"Heat Capacity"DeltaT
Thus, this quantity for water is c_(s,H_2O(l)) = "4.184 J/g"^@ "C" at 25^@ "C" regardless of the sample size, for copper is c_(s,Cu(s)) = "0.385 J/g"^@ "C" at 25^@ "C" regardless of the sample size, etc.
