The 2-digit number is 26:
26 - 1 = 25 is a square number.
26 + 1 = 27 is a cube number.
How to find the number?
Here we want to find a 2-digit number N, such that:
- N + 1 is a cube number.
- N - 1 is a square number.
To do that, we can just create a list of cubic and square numbers of 2 digits, these are:
Square numbers:
4*4 = 16
5*5 = 25
6*6 = 36
etc...
Cube numbers:
3*3*3 = 27
4*4*4 = 64
etc...
Now, we can see that 25 is a square number and 27 is a cube number, then our 2-digit number can be 26.
Because:
26 - 1 = 25 is a square number.
26 + 1 = 27 is a cube number.
If you want to learn more about square numbers;
https://brainly.com/question/21694652
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