The dimensions of a metal block are 2.25 m by 1.5 m by 27 cm.

$1 \mathrm{~m}=100 \mathrm{~cm}$

Volume of the original block $=225 \times 150 \times 27=911250 \mathrm{~cm}^{3}$

Length of the edge of one cube $=45 \mathrm{~cm}$

Then volume of one cube $=45^{3}=91125 \mathrm{~cm}^{3}$

$\therefore$ Total number of blocks that can be cast $=\frac{\text { volume of the block }}{\text { volume of one cube }}=\frac{911250}{91125}=10$