Here is some of the verses about David (Dawood) in the Quran:
As a military leader and king:
2:251 By Allah's will they routed them; and David slew Goliath; and Allah gave him power and wisdom and taught him whatever (else) He willed. And did not Allah Check one set of people by means of another, the earth would indeed be full of mischief: But Allah is full of bounty to all the worlds.
فَهَزَمُوهُم بِإِذْنِ اللّهِ وَقَتَلَ دَاوُدُ جَالُوتَ وَآتَاهُ اللّهُ الْمُلْكَ وَالْحِكْمَةَ وَعَلَّمَهُ مِمَّا يَشَاء وَلَوْلاَ دَفْعُ اللّهِ النَّاسَ بَعْضَهُمْ بِبَعْضٍ لَّفَسَدَتِ الأَرْضُ وَلَـكِنَّ اللّهَ ذُو فَضْلٍ عَلَى الْعَالَمِينَ
As a devout worshipper:
34:10 We bestowed Grace aforetime on david from ourselves: "O ye Mountains! Sing ye back the Praises of Allah with him! and ye birds (also)! And We made the iron soft for him;
وَلَقَدْ آتَيْنَا دَاوُودَ مِنَّا فَضْلًا يَا جِبَالُ أَوِّبِي مَعَهُ وَالطَّيْرَ وَأَلَنَّا لَهُ الْحَدِيدَ
As a Just leader:
38:26 O david! We did indeed make thee a vicegerent on earth: so judge thou between men in truth (and justice): Nor follow thou the lusts (of thy heart), for they will mislead thee from the Path of Allah. for those who wander astray from the Path of Allah, is a Penalty Grievous, for that they forget the Day of Account.
يَا دَاوُودُ إِنَّا جَعَلْنَاكَ خَلِيفَةً فِي الْأَرْضِ فَاحْكُم بَيْنَ النَّاسِ بِالْحَقِّ وَلَا تَتَّبِعِ الْهَوَى فَيُضِلَّكَ عَن سَبِيلِ اللَّهِ إِنَّ الَّذِينَ يَضِلُّونَ عَن سَبِيلِ اللَّهِ لَهُمْ عَذَابٌ شَدِيدٌ بِمَا نَسُوا يَوْمَ الْحِسَابِ
