841*. A natural number is equal to the cube of the number of its thousands. Find all such numbers.
$\triangle$ Let's denote the desired number as $1000 x+y$, where $x-$ is the number of its thousands, and $y<1000$. Estimate the number $k$ from above:

$$
k=\frac{y}{x}<\frac{1000}{31}<33
$$

However, the sum $1000+k$ must be a square of a natural number. Only $k=24$ fits:

$$
1000+k=1024=32^{2}
$$

Therefore, $x=32$. Let's find $y$ as well: $y=k x=24 \cdot 32=768$.

Answer: 32768.