I think this is the only place in the Torah where "Yehoshua" is spelled maleh - with a full vav (Shuruk). I think there are other places in Tanac"h where a similar thing occurs, but, I don't know for certain.
Why is his name spelled this way, here?
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Sign up to join this communityMidrash Chaseiros VeYeseiros says it's written maleh in three places. Here it's because he acquired six crowns (the value of the letter vav): beauty, strength, wealth, wisdom, leadership and prophecy (Cf. Avos 6:8). This is also stated in Midrash Minyanin.
The other two are Joshua 24:31 (although if you follow the link it's chaser) and Judges 2:7, teaching us that because of Yehoshua the people served Hashem with a full heart.
Taamei Mesores HaMikra by Rav Yehudah HaChossid says that it's written maleh because it was at this point that Yehoshua was commanded regarding Yisroel (לפי שאז צוהו על אודות ישר', לכך מלא; I don't get it). He then adds that from when they entered the land until King David was King is 397 years, the numerical value of יהושוע.
Chomas Anach by the Chidah ad. loc. says that the verse is making a connection between when the sun stopped for Yehoshua and when it stopped for Moshe (see Avodah Zara 25a). The verse is written maleh because Yehoshua's name became greatened when the sun stopped for him.
Chasam Sofer in Derashos III says it's because Moshe treated Yehoshua with a good eye. He made him "full and packed" (מלא וגדוש). See Sifrei Bamidbar 141.
Maharil Diskin ad. loc. lists 30 times Yehoshua's name appears in the Torah. He says it should appear 31 times, corresponding to the 31 Canaanite Kings he conquered. This time is the 31st time, so it is written maleh (also don't get it...also why here and not the last time in sefer Devarim).