|Easton's Bible Dictionary|
(1.) The residence of Adoni-bezek, in the lot of Judah (Judges 1:5). It was in the mountains, not far from Jerusalem. Probably the modern Bezkah, 6 miles south-east of Lydda.
(2.) The place where Saul numbered the forces of Israel and Judah (1 Samuel 11:8); somewhere in the centre of the country, near the Jordan valley. Probably the modern Ibzik, 13 miles north-east of Shechem.
Int. Standard Bible Encyclopedia
be'-zek (bezeq; Bezek, Codex Vaticanus, Abiezek):
(1) The city of Adoni-bezek taken by Judah and Simeon (Judges 1:4 f), in the territory allotted to Judah. It is somewhat doubtfully identified with Bezqah, about 3 miles Northeast of Gezer.
(2) The place where Saul marshaled his army before marching to the relief of Jabesh-gilead (1 Samuel 11:8). Eusebius, Onomasticon speaks of two villages of this name 17 Roman miles from Shechem, on the way to Scythopolis. No doubt Khirbet Ibziq is intended. Here, or on the neighboring height, Ras Ibziq, a mountain 2,404 ft. above sea level, the army probably assembled.
Bezek (3 Occurrences)
Judges 1:4 Judah went up; and Yahweh delivered the Canaanites and the Perizzites into their hand: and they struck of them in Bezek ten thousand men. (WEB KJV JPS ASV BBE DBY WBS YLT NAS RSV NIV)
Judges 1:5 They found Adoni-Bezek in Bezek; and they fought against him, and they struck the Canaanites and the Perizzites. (WEB KJV JPS ASV DBY WBS YLT NAS RSV NIV)
1 Samuel 11:8 He numbered them in Bezek; and the children of Israel were three hundred thousand, and the men of Judah thirty thousand. (WEB KJV JPS ASV BBE DBY WBS YLT NAS RSV NIV)