Yes; heat capacity, in units of #"J/"^@ "C"#, or #"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_s#, in units of #"J/g"^@ "C"# or #"J/g"cdot"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.
