To simplify the expression

\[
B = 27(a+b+c)^3 - (2a+3b-2c)^3 - (2b+3c-2a)^3 - (2c+3a-2b)^3,
\]

let's analyze each term:

1. **Expanding the cubes**:
- \( (a+b+c)^3 \) will expand according to the binomial theorem.
- Each of the other three cubes, such as \( (2a+3b-2c)^3 \), will also expand, but they involve combinations of \( a, b, \) and \( c \).

2. **Using known identities**:
The expression resembles an identity related to symmetric sums, or it can relate to properties of polynomial roots or transformation symmetries.

3. **Rearranging terms**:
You can regroup and analyze contributions from each polynomial.

4. **Substituting values**:
Testing specific values (like \( a = 1, b = 1, c = 1 \) or \( a = 0, b = 0, c = 0 \)) may demonstrate the identity holds in particular cases.

To find a general result, one might check the distributions of each polynomial or relate it to symmetry in them.

The full expansion would be lengthy, but you'd generally be looking for terms to cancel due to symmetry properties. Alternatively, you could compute some special cases to reveal more about \( B \).

Overall, after careful expansion and combination, this expression likely simplifies to zero or exhibits a symmetric property as a polynomial in \( a, b, c \).