Let \(N \in \mathbb{N}\) be a number with digits \(a_k\), where \(a_0\) is the least significant digit and \(n\) is the most significant digit.

Find all numbers with the following property:

$$N = \sum_{k=0}^n a_k \cdot 10^k = \sum a_k^3$$

## Lower and upper bounds

- The lower bound is \(0\)
- The upper bound is \(2916\) since \(4\cdot 9^3 = 2916\)

You can find better upper bounds, but as we've just reduced the possible number space to only 2917 numbers, it doesn't really matter.

## Find all solutions

```
#!/usr/bin/env python3
def find_sum_of_cubes():
"""Returns all numbers N with the following property
N = \sum_{k=0}^n a_k \cdot 10^k = \sum a_k^3
"""
def has_sum_of_cubes_property(n):
digits = map(int, list(str(n)))
return sum(map(lambda n: n**3, digits)) == n
return list(filter(has_sum_of_cubes_property, range(2917)))
if __name__ == "__main__":
print(find_sum_of_cubes())
```

which gives

```
[0, 1, 153, 370, 371, 407]
```