Find the smallest natural number by which $1458$ must be divided so that the quotient is a perfect cube.

In the five digit number $1b6a3, a$ is the greatest single digit perfect cube and twice of it exceeds $b$ by $7$. Then the sum of the number and its cube root is _____. 

Three numbers are in the ratio $2:3:5$ to one another. The sum of their cubes is $54880$. The numbers are _____.

The cube of a $2$-digit number will contain _____.

The cube of an odd natural number is always _____.

The length of each side of a cubical box is $2.4 \mathrm{m}$. Its volume is _____.

The unit's digit of the cube of a number is $9$. The unit's digit of it cube root is _____.

The cube of a number $x$ is nine times of $x$, then find $x$ (where $x\ne 0$ and $x\ne -3$).

Two cubes have volumes in the ratio $1:27$. The ratio of the area of the face of one to that of the other is _____.