Is one squared less than one cubed?

They are the same.

1^n=1, or 1 to any power is 1.
1^2=1*1=1
1^3=1*1*1=1
They are equivalent.

I’m sure that you meant +1, but just for the sake of discussion, -1 squared is more than -1 cubed: 1 > -1.

On what planet? On earth, they are equivalent. On Tralfamadore, they are not.

Here is a way of looking at it.
For numbers x greater than 1, x^2 < x^3.
For numbers x greater than 0 but less than 1, x^2 > x^3. For example (½)^3 = ½(½)^2, meaning that (½)^3 is half of (½)^2, which makes it smaller.

For both 0 and 1, x^3 = x^2.
If we write x^3 = x^2, then x^3 – x^2 = 0. x^2(x – 1) = 0, which has solutions of x = 0 and x = 1.

No, 1 is not less than or greater than 1.