Three numbers are to one another 2 : 3 : 4.

Solution:

Let the numbers be 2x, 3x and 4x.

According to the question:​

$(2 x)^{3}+(3 x)^{3}+(4 x)^{3}=0.334125$

$\Rightarrow 8 x^{3}+27 x^{3}+64 x^{3}=0.334125$

$\Rightarrow 8 x^{3}+27 x^{3}+64 x^{3}=0.334125$\

$\Rightarrow 99 x^{3}=0.334125$

$\Rightarrow x=\sqrt[3]{\frac{3375}{1000000}}$

$\Rightarrow x=\frac{\sqrt[3]{3375}}{\sqrt[3]{1000000}}$

$\Rightarrow x=\frac{15}{100}=0.15$

Thus, the numbers are:

$2 \times 0.15=0.30$

$3 \times 0.15=0.45$

$4 \times 0.15=0.60$