Calculate the Value of a Cubic Expression

Let the real numbers $a$, $b$, and $c$ satisfy the relationships:

$a + b + c = 15$

$ab + bc + ca = 53$

Determine the value of the expression:

$$a^3 + b^3 + c^3 - 3abc$$

Use the identity which relates the sum of cubes to the sum and products of the variables:

$$a^3 + b^3 + c^3 - 3abc = (a + b + c)((a + b + c)^2 - 3(ab + ac + bc))$$