Solution

$$\displaystyle 819=3\times 3\times 7\times 13$$

$$\Rightarrow$$ $$\displaystyle{ \left( 819 \right) }^{ 3 }={ \left( 3 \right) }^{ 3 }\times { \left( 3 \right) }^{ 3 }\times { \left( 7 \right) }^{ 3 }\times { \left( 13 \right) }^{ 3 }$$

$$\displaystyle =3\times 3\times 3\times 3\times 3\times 3\times 7\times 7\times 7\times 13\times 13\times 13$$

$$\displaystyle =27\times 27\times 343\times 2197$$

$$\displaystyle =549353259$$

$$\displaystyle \therefore $$ The cube of $$819 = 549353259.$$