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By employing the generating function of $c\\phi_{6}(3n+1)$ found by Hirschhorn, we prove that $c\\phi_{6}(27n+16)\\equiv 0$ (mod 243). This confirms a conjecture of E.X.W. Xia. We also find a congruence relation $c\\phi_{6}(81n+61) \\equiv 3 c\\phi_{6}(9n+7)$ (mod 243). Moreover, we show that $c\\phi_{6}(81n+61) \\equiv 0$ (mod 81), $c\\phi_{6}(243n+142) \\equiv 0$ (mod 243) and $c\\phi_{6}(729n+ 547) \\equiv 0$ (mod 243). 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