1256 - [256:2^3 + (15^2 : 3^2 + 6.6^2)]

First, let's simplify the expressions inside the parentheses:

15^2 = 225
3^2 = 9
6.6^2 = 43.56

Now, let's substitute these values back into the expression:

1256 - [256:2^3 + (225 : 9 + 43.56)]

Next, let's simplify the expression inside the parentheses:

256:2^3 = 256:8 = 32
225:9 = 25
43.56 remains the same

Now, let's substitute these values back into the expression:

1256 - [32 + (25 + 43.56)]

Next, let's simplify the expression inside the parentheses:

25 + 43.56 = 68.56

Now, let's substitute this value back into the expression:

1256 - [32 + 68.56]

Next, let's simplify the expression inside the brackets:

32 + 68.56 = 100.56

Now, let's substitute this value back into the expression:

1256 - 100.56

Finally, let's subtract:

1256 - 100.56 = 1155.44

Therefore, 1256 - [256:2^3 + (15^2 : 3^2 + 6.6^2)] = 1155.44