This is the 2263rd most frequent Japanese word.
輝い
"輝い" is not a proper form in Japanese. You may mean "輝き" (kagayaki), which means "brightness" or "radiance."
In this sentence, "輝いている" is used as a verb describing the state of shining brightly.
彼の目が輝いている。
His eyes are shining.
"輝いた" is used here to describe the lights of the city as being bright and radiant.
輝いた街の灯が夜空を彩る。
The shining city lights decorate the night sky.
"輝かせる" is used in a causative form to express making or causing something to shine as a metaphorical description.