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MathNet 2019-part-08 — 179 problems (EN–VI) Question 65

Math Olympiad Vault · MathNet 2019-part-08 — 179 problems (EN–VI)

Question 65

In 2019, a team, including professor Andrew Sutherland of MIT, found three cubes of integers which sum to $42$:
$$
42 = \left(-8053873881207597\_\right)^3 + (80435758145817515)^3 + (12602123297335631)^3
$$
One of the digits, labeled by an underscore, is missing. What is that digit?