Let's simplify the expression step by step:
The expression is:
\[ \frac{1}{8} \times \left(-\frac{1}{8} - 8\right) + \left(-\frac{1}{8} - 6\right) \times \left(-\frac{1}{8} - 6\right) \]
First, calculate \(-\frac{1}{8} - 8\):
\[ -\frac{1}{8} - 8 = -\frac{1}{8} - \frac{64}{8} = -\frac{1 + 64}{8} = -\frac{65}{8} \]
Now, substitute this back into the expression:
\[ \frac{1}{8} \times \left(-\frac{65}{8}\right) + \left(-\frac{1}{8} - 6\right) \times \left(-\frac{1}{8} - 6\right) \]
Now calculate \(\frac{1}{8} \times -\frac{65}{8}\):
\[ \frac{1}{8} \times -\frac{65}{8} = -\frac{65}{64} \]
Next, calculate \(-\frac{1}{8} - 6\):
\[ -\frac{1}{8} - 6 = -\frac{1}{8} - \frac{48}{8} = -\frac{49}{8} \]
Now we need to compute \(\left(-\frac{49}{8}\right) \times \left(-\frac{49}{8}\right)\):
\[ \left(-\frac{49}{8}\right)^2 = \frac{49^2}{8^2} = \frac{2401}{64} \]
Now we can put it all back into the original expression:
\[ -\frac{65}{64} + \frac{2401}{64} \]
This is equivalent to:
\[ \frac{-65 + 2401}{64} = \frac{2336}{64} \]
Finally, simplify \(\frac{2336}{64}\):
\[ 2336 \div 64 = 36.5 \]
Thus, the final answer is:
\[ \boxed{36.5} \]