If $\dfrac{a}{b} = \dfrac{b}{c} = \dfrac{c}{d}$, then $\dfrac{b^3 + c^3 + d^3}{a^3 + b^3 + c^3}$ is equal to:

1. $\dfrac{a}{b}$

2. $\dfrac{b}{c}$

3. $\dfrac{c}{d}$

4. $\dfrac{d}{a}$

Let $\dfrac{a}{b} = \dfrac{b}{c} = \dfrac{c}{d}$ = k where k is the constant ratio.

Therefore,

c = dk

b = ck = (dk)k = dk²

a = bk = (dk²)k = dk³

k³ = $\dfrac{a}{d}$

Substitute value of a,b and c in $\dfrac{b^3 + c^3 + d^3}{a^3 + b^3 + c^3}$, we get:

$\Rightarrow \dfrac{(dk^2)^3 + (dk)^3 + d^3}{(dk^3)^3 + (dk^2)^3 + (dk)^3} \\[1em] \Rightarrow \dfrac{d^3k^6 + d^3k^3 + d^3}{d^3k^9 + d^3k^6 + d^3k^3} \\[1em] \Rightarrow \dfrac{d^3(k^6 + k^3 + 1)}{d^3k^3(k^6 + k^3 + 1)} \\[1em] \Rightarrow \dfrac{1}{k^3} \\[1em] \Rightarrow \dfrac{1}{\dfrac{a}{d}} \\[1em] \Rightarrow \dfrac{d}{a}.$

Hence, option 4 is the correct option.