A regular cube has a resistance R between any two faces. If it is splitted into 27 identical small cubes then the resistance between any two faces of smaller cube

Resistance of a cubical conductor

$\mathrm{R}=\mathrm{\rho }\frac{\mathrm{l}}{{\mathrm{l}}^2}=\frac{\mathrm{\rho }}{\mathrm{l}}$

$R\propto \frac{1}{l}$

now  volume of the big cube must be equal to volume of 27 small cube 

$$\begin{gathered} {\mathrm{l}}^3=27{\mathrm{a}}^3 \\ \mathrm{a}=\frac{\mathrm{l}}{3} \end{gathered}$$

As the size of the small cube is decreases to three times resistance increases to 3R