A natural number is called a square if it can be written as the product of two equal numbers. For example, 9 is a square, since $9=3 \times 3$. The first squares are 1, 4, 9, 16, 25, ... A natural number is called a cube if it can be written as the product of three equal numbers. For example, 8 is a cube, since $8=2 \times 2 \times 2$. The first cubes are $1,8,27,64,125 \ldots$

One day, the square and cube numbers decided to go on strike. This is how the other natural numbers had to take new positions:

![](https://cdn.mathpix.com/cropped/2024_05_01_d18780f0fd52e0502cf8g-21.jpg?height=113&width=1082&top_left_y=763&top_left_x=544)

a) What is the number that ended up in the $12^{\text {th }}$ position?

b) What are the numbers less than or equal to 2013 that are both squares and cubes?

c) What is the new position occupied by the number 2013?

d) Find out which number ended up in the $2013^{\text{th}}$ position.