the square of a number is the second power of the number. the cube of a number is the third power of the number . explain why these names ar

Probably comes from a geometrical interpretation.  A square of side length L has an area of L².  A cube of side length L has a volume of L³.

the square of a number is the second power of the number.       $$x^2$$

the cube of a number is the third power of the number . explain why these names are reasonable      $$x^3$$

Because they are the same thing.