The Song Of Torah

  ועתה כתבו לכם את השירה הזאת

The Rambam Laws of Talmud Torah (3:13) says אַף עַל פִּי שֶׁמִּצְוָה לִלְמֹד בַּיּוֹם וּבַלַּיְלָה אֵין אָדָם לָמֵד רֹב חָכְמָתוֹ אֶלָּא בַּלַּיְלָה. לְפִיכָךְ מִי שֶׁרָצָה לִזְכּוֹת בְּכֶתֶר הַתּוֹרָה יִזָּהֵר בְּכָל לֵילוֹתָיו וְלֹא יְאַבֵּד אֲפִלּוּ אֶחָד מֵהֶן בְּשֵׁנָה וַאֲכִילָה וּשְׁתִיָּה וְשִׂיחָה וְכַיּוֹצֵא בָּהֶן אֶלָּא בְּתַלְמוּד תּוֹרָה וְדִבְרֵי חָכְמָה. אָמְרוּ חֲכָמִים אֵין רִנָּה שֶׁל תּוֹרָה אֶלָּא בַּלַּיְלָה שֶׁנֶּאֱמַר (.איכה ב יט) "קוּמִי רֹנִּי בַלַּיְלָה" וכו  Why does the Rambam put such emphasis on learning Torah at night?
The Gemorah in Megillah (3a) says the malach told Yehoshua that God was angry at him for not offering the evening tammid and not learning at night.  Yehoshua asked which was worst and the malach told him עתה באתי which the Gemorah understands is a hint to Torah.  How is it a hint to Torah?  Tosfos explains that the word עתה is linked to the word עתה in this possuk,   ועתה כתבו לכם את השירה הזאת.  Why is this possuk the one that the malachuses to  tells Yehoshua the hint to Torah when its not the possuk of the obligation ot learning Torah?  The Ponovitcher Rav explains that thecontext of the possuk was in the time of war of conquering Eretz Yisroel.  There were plenty of things that Yehoshua had to take care of and make sure were right to ensure safety and success in the war.  His excuse for missing night seder would have been one of the best in history.  The possuk of the obligation for learning Torah wouldn't have been reason to chastise Yehoshua.  However, if Torah is a shirah, its the joy of your life, then you make time for it.  Despite the myriad of things Yehoshua had to get done, as a shirah, there are no excuses (printed in back of Zichron Shmuel sicha 14.)   
Rav Yeruchem Olshin says that is the peshat in the Rambam.  The time of day is when people tend to the work that they have to do.  One's learning at that time may be because that is his job.  It is at night when one people generally relax and unwind.  In one learns during that time, that proves that his learning isn't something he "does", but rather that is the person's joy in life, that proves it is a shirah.
The Rambam cites the possuk of קוּמִי רֹנִּי בַלַּיְלָה.  A רנה is a song that burst forth from a person (see Even Ezra there,) it is the song of Torah that illuminates the darkness of the night.  It is the "voluntary" Torah that is the song of the soul.