To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints in terms of these variables.

Let's define the variables as follows:
- $x_1$ represents 'milligrams of vitamin B2'
- $x_2$ represents 'milligrams of vitamin B1'
- $x_3$ represents 'milligrams of zinc'

The objective function to maximize is given by:
\[ 1 \cdot x_1^2 + 3 \cdot x_1 \cdot x_2 + 7 \cdot x_2^2 + 6 \cdot x_2 \cdot x_3 + 2 \cdot x_3^2 + 8 \cdot x_1 + 8 \cdot x_2 \]

The constraints are:
1. $13x_1$ (energy stability index of milligrams of vitamin B2)
2. $11x_2$ (energy stability index of milligrams of vitamin B1)
3. $4x_3$ (energy stability index of milligrams of zinc)
4. $13x_1 + 11x_2 \leq 111$
5. $(13x_1)^2 + (4x_3)^2 \leq 65$
6. $13x_1 + 11x_2 + 4x_3 \leq 51$
7. $x_1 + x_2 + x_3 \leq 51$ (This constraint seems to be a repetition or misinterpretation since it doesn't involve the energy stability indices directly as the others do, but we'll include it as per the description)
8. $x_1$, $x_2$, and $x_3$ can be fractional.

Symbolic representation:
```json
{
  'sym_variables': [('x1', 'milligrams of vitamin B2'), ('x2', 'milligrams of vitamin B1'), ('x3', 'milligrams of zinc')],
  'objective_function': '1*x1**2 + 3*x1*x2 + 7*x2**2 + 6*x2*x3 + 2*x3**2 + 8*x1 + 8*x2',
  'constraints': [
    '13*x1 <= 128', 
    '11*x2 <= 128', 
    '4*x3 <= 128', 
    '13*x1 + 11*x2 <= 111', 
    '(13*x1)**2 + (4*x3)**2 <= 65', 
    '13*x1 + 11*x2 + 4*x3 <= 51', 
    'x1 + x2 + x3 <= 51'
  ]
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define the variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B2")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B1")
x3 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_zinc")

# Define the objective function
m.setObjective(1*x1**2 + 3*x1*x2 + 7*x2**2 + 6*x2*x3 + 2*x3**2 + 8*x1 + 8*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(13*x1 <= 128)
m.addConstr(11*x2 <= 128)
m.addConstr(4*x3 <= 128)
m.addConstr(13*x1 + 11*x2 <= 111)
m.addConstr((13*x1)**2 + (4*x3)**2 <= 65)
m.addConstr(13*x1 + 11*x2 + 4*x3 <= 51)
m.addConstr(x1 + x2 + x3 <= 51)

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of Vitamin B2: {x1.x}")
    print(f"Milligrams of Vitamin B1: {x2.x}")
    print(f"Milligrams of Zinc: {x3.x}")
else:
    print("No optimal solution found")
```