To calculate this expression, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, let's calculate 12^3:
12^3 = 12 * 12 * 12 = 1,728

Now, let's calculate 3.3^3:
3.3^3 = 3.3 * 3.3 * 3.3 = 35.937

Finally, let's multiply the two results together:
1,728 * 35.937 = 62,100.336

Therefore, 12^3.3^3 is approximately equal to 62,100.336.