The description of David, "reddish with beautiful eyes" ("אַדְמוֹנִי עִם יְפֵה עֵינַיִם") equals "kingdom" (malchut, מלכות, 496). That's what it takes to be a king and rule over a kingdom.
The entire verse, "And he sent and brought him, and he was reddish with beautiful eyes and goodly appearance, and God said, Arise anoint him for this is he" ("וַיִּשְׁלַח וַיְבִיאֵהוּ וְהוּא אַדְמוֹנִי עִם יְפֵה עֵינַיִם וְטוֹב רֹאִי וַיֹּאמֶר י-הוה קוּם מְשָׁחֵהוּ כִּי זֶה הוּא") equals 4 times kingdom, 4 times "reddish with beautiful eyes" (corresponding, in Kabbalah, to the manifestation of the sefirah of kingdom in each of the four worlds, Emanation, Creation, Formation, Action).
Another indication that the phrase "reddish with beautiful eyes" is the kernel essence of the entire verse is that the verse comprises 16 words while the phrase "reddish with beautiful eyes" comprises 16 letters. 16 = 42. The phrase "reddish with beautiful eyes" comprises 4 words (22, the root of 16). These are striking examples of self-reference.
The "seal" of the verse is "for this is he!" (כי זה הוא). This (זה) = he (הוא). The commentaries explain this to mean that David's revealed appearance, his manifestation in This World ("this") exactly reflects his hidden essence, his manifestation in the World to Come ("he"). Indeed, "this is he" (זה הוא) equals "David" as his name appears often in the Bible: דויד. David's reddishness derives from his "this" while his beautiful eyes derive from his "he." First Samuel only saw his "this" but not the inner-inclusion of his "he" with his "this."
Previously God had chastised Samuel, who mistakenly thought that David's older brother was the one to be anointed, saying "look not at his countenance… for God sees not as man sees, for man looks at the outward appearance, but God looks at the heart" ("אַל תַּבֵּט אֶל מַרְאֵהוּ… כִּי הָאָדָם יִרְאֶה לַעֵינַיִם וַה' יִרְאֶה לַלֵּבָב").
But Samuel was unable to fully internalize God's chastisement (thus demonstrating God's very assessment of the difference between Him and man). Once again his initial impression of David was mistaken; he saw only his "this" but not his "he."
"Reddish with beautiful eyes [= kingdom] and goodly appearance" (אדמוני עם יפה עינים וטוב ראי, 730) together with "this is he" (24) = 754 = 13 times 58. 13 = "one" (אחד) and 58 = "grace" (חן), symmetric beauty. In small numbering, "grace" itself equals "one." "But God looks at the heart" (וַי-הוה יִרְאֶה לַלֵּבָב) equals 312 = 13 (one) times 24. 24 = "this is he" (זה הוא) or David (דויד).
"Reddish with beautiful eyes and goodly appearance" together with "for this is he" (כי זה הוא) equals 784 = 282 (28 = 2 times 14, David, דוד).
Skipping every other letter in the phrase "reddish with beautiful eyes" divides kingdom, 496, into 196, 142 (David squared) and 300, the triangle of 24 (= "this is he")! The full value, 496, is itself the triangle of 31 (God's Name El, א-ל). Thus, we arrive at the mathematical expression: 142 plus triangle 24 = triangle 31, which generalizes to:
(4n plus 2)2 plus triangle (7n plus 3) = triangle (9n plus 4)
This, then, is a kingly mathematical expression!