Simplify:
$$\frac{0.1\times 0.1\times 0.1+0.3\times 0.3\times 0.3}{0.3\times 0.3-0.3\times 0.1+0.1\times 0.1}$$

Let $a=0.1$ and $b=0.3$.The given expression can be written in terms of $a$ and $b$ as:
$$\frac{a^3+b^3}{b^2-ba+a^2}$$
We know the algebraic identity for the sum of cubes:
$$a^3+b^3=(a+b)(a^2-ab+b^2)$$
Substituting this identity into the expression:
$$\frac{(a+b)(a^2-ab+b^2)}{a^2-ab+b^2}=a+b$$
Now, substituting the values of $a$ and $b$ back into the simplified expression:
$$a+b=0.1+0.3=0.4$$