Roberto De Zerbi's team sit third in Ligue 1, eight points off leaders Lens, and the Italian showed his desire to collect some silverware by fielding a strong side for their clash with the unfancied Norman outfit.
English international Mason Greenwood and French 2018 World Cup winner Benjamin Pavard started for Marseille in Caen, where the match took place at the local third-division side's stadium because Bayeux's home ground was not big enough.
First-half goals from Angel Gomes, Hamed Junior Traore, Greenwood and Amine Gouiri put Marseille in cruise control.
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The former Manchester United forward Greenwood scored his second early in the second period, before Gouiri again netted, as did CJ Egan-Riley and Neal Maupay.
Greenwood then completed his hat-trick in the 90th minute.
Marseille will next face fellow Ligue 1 club Rennes in the last 16, following the draw earlier on Tuesday.
French Cup last 16 draw:
Toulouse vs Amiens
Strasbourg vs Monaco
Reims vs Le Mans
Nice vs Montpellier
Lyon vs Laval
Marseille vs Rennes
Lorient vs Paris FC
Troyes vs Lens