Let $$f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3), \; x \in \mathbb{R}$$. Then $$f'(10)$$ is equal to _______.

Let $$f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3)$$.

Let $$f'(1) = a$$, $$f''(2) = b$$, $$f'''(3) = c$$.

$$f(x) = x^3 + ax^2 + bx + c$$

$$f'(x) = 3x^2 + 2ax + b$$

$$f''(x) = 6x + 2a$$

$$f'''(x) = 6$$

From $$f'''(3) = c$$: $$c = 6$$.

From $$f''(2) = b$$: $$12 + 2a = b$$.

From $$f'(1) = a$$: $$3 + 2a + b = a$$, so $$b = -a - 3$$.

From the two equations for b:

$$12 + 2a = -a - 3$$

$$3a = -15$$

$$a = -5$$

$$b = -(-5) - 3 = 2$$

$$f'(x) = 3x^2 - 10x + 2$$

$$f'(10) = 300 - 100 + 2 = 202$$

The answer is $$\boxed{202}$$.