Classify the following numbers as square, cube, or triangular numbers: 1, 8, 9, 10, 15, 16, 25, 125.

Here is the classification of the given numbers:

• Square numbers are integers that are the square of another integer ($n^2$).

  • $1 = 1^2$
  • $9 = 3^2$
  • $16 = 4^2$
  • $25 = 5^2$
  • Therefore, the square numbers are: $\boxed{\text{1, 9, 16, 25}}$

• Cube numbers are integers that are the cube of another integer ($n^3$).

  • $1 = 1^3$
  • $8 = 2^3$
  • $125 = 5^3$
  • Therefore, the cube numbers are: $\boxed{\text{1, 8, 125}}$

• Triangular numbers are numbers that can form an equilateral triangle, represented by the formula $T_n = \frac{n(n+1)}{2}$.

  • $1 = \frac{1(1+1)}{2}$
  • $10 = \frac{4(4+1)}{2}$
  • $15 = \frac{5(5+1)}{2}$
  • Therefore, the triangular numbers are: $\boxed{\text{1, 10, 15}}$