Sourajit makes a cuboid of plasticine of sides $5 \mathrm{cm}, 2 \mathrm{cm}, 5 \mathrm{cm}$. How many such cuboids will he need to form a cube?

Given that the cube's side is $5 \mathrm{cm},2 \mathrm{cm},5 \mathrm{cm}$

As a result, the cube's volume is $=5\times 2\times 5=50$

The principal factorization is $50=2\times 5\times 5$

The numbers $2,5$ and $5$ cannot be grouped into equal-factor triples.

As a result, we will multiply $50$ by $2\times 2\times 5=20$ to obtain a perfect square

As a result, $20$ cuboid is required.