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Number theory Difficulty 1.0 Junior Find the answer United Kingdom

Pablo has 100 identical small cubes. He uses some of them to build the largest possible solid cube. How many of the small cubes are left over?

(A) $16$ (B) $27$ (C) $36$ (D) $73$ (E) $92$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.