$1^3=1$

$1^3+2^3=9$

$1^3+2^3+3^3=36$

$1^3+2^3+3^3+4^3=100$

$1^3+2^3+3^3+4^3+5^3=225$

$1^3+2^3+3^3+4^3+5^3+6^3=441$

Use the pattern to answer the below given question: 

The value of ${\left(1+2+3+4\right)}^2+1=$  .

Find the smallest number by which $2560$ must be multiplied so that the product is a perfect cube.

Evaluate: $(0.05{)}^3$

Evaluate: ${\left(8\right)}^3$

Check whether, $1000$ is a cube of an even number or not?

Check whether $3375$ is a perfect cube or not? If it is a perfect cube, find the number whose cube is $3375$.

Evaluate: ${\left(1\frac{3}{10}\right)}^3$

What is the smallest number by which $1600$ must be divided so that the quotient is a perfect cube?

Find the smallest number by which $8788$ must be divided so that the quotient is a perfect cube.

Find the smallest number by which $1323$ must be multiplied so that the product is a perfect cube.