Simplify the expression:
15×15×15+3×15×12×12−3×15×15×12−12×12×12

Let a=15 and b=12.
Rewriting the expression in terms of a and b:

Expression=a
3
+3ab
2
−3a
2
b−b
3

Rearranging the terms:

Expression=a
3
−3a
2
b+3ab
2
−b
3

We recognize this as the standard algebraic identity for (a−b)
3
:

(a−b)
3
=a
3
−3a
2
b+3ab
2
−b
3

Substituting the values of a and b:

Expression=(15−12)
3

Expression=(3)
3
=27