Problem
Find the length of one side of a cube that is $1881676371789154860897069 \ cubic \ inches$.
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Solution
When $1881676371789154860897069$ is decomposed into prime factors,
$$3^6×3607^3×3803^3=(3^2×3607×3803)^3. \qquad [*]$$
Therefore, the length of one side of the cube is
$$\sqrt[3]{1881676371789154860897069}=3^2×3607×3803=123456789.$$
$$(Answer) \quad 123456789 \quad inches.$$
$[*]$ The following high-precision online calculation site was used:
Reference
Yoshikazu Yamakawa, ed. (1997) Okayama ken no Sangaku (Sangaku in Okayama Prefecture), p.27; pp.398-399.