According to the question,

The radius of each spherical lead shot $=r=4/2=2cm$

Volume of each spherical lead shot $=4/3\pi {{r}^{3}}=4/3\pi {{2}^{3}}c{{m}^{3}}$

Edge of the cube $=44cm$

Volume of the cube $={{44}^{4}}c{{m}^{3}}$

Number of spherical lead shots $=$ Volume of cube/ Volume of each spherical lead shot

$=44\times 44\times 44/\left( 4/3\pi {{2}^{3}} \right)$

$=2541$