It is given in the question that,

A solid sphere of radius, $R=8cm$

With this sphere, we have to make spherical balls of radius $r=1cm$

Now, assume that the number of balls made as n

As, we know that

Formula for volume of the sphere $=4/3\pi {{r}^{3}}$

The volume of the solid sphere $=$ sum of the volumes of n spherical balls.

$n\times 4/3\pi {{r}^{3}}=4/3\pi {{R}^{3}}$

$n\times 4/3\pi {{\left( 1 \right)}^{3}}=4/3\pi {{\left( 8 \right)}^{3}}$

$n={{8}^{3}}=512$

Hence, 512 balls can be made of radius $1cm$ each with a solid sphere of radius $8cm$.