Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm,

We have,

Edges of the cubes: $a_{1}=3 \mathrm{~cm}, a_{2}=4 \mathrm{~cm}$ and $a_{3}=5 \mathrm{~cm}$

Let the edge of the new cube be $a$.

Now,

Volume of the new cube $=a_{1}^{3}+a_{2}^{3}+a_{3}{ }^{3}$

$\Rightarrow a^{3}=3^{3}+4^{3}+5^{3}$

$\Rightarrow a^{3}=27+64+125$

$\Rightarrow a^{3}=216$

$\Rightarrow a=\sqrt[3]{216}$

$\therefore a=6 \mathrm{~cm}$

So, the edge of the new cube so formed is 6 cm.