From thele (the nipple); to suckle, (by implication) to suck -- (give) suck(-ling).
Thayer's Greek Lexicon
Strong's 2337: θηλάζω
θηλάζω; 1 aorist ἐθήλασα; (θηλή a breast (cf. Peile, Etym., p. 124f));
1. transitive, to give the breast, give suck, to suckle: Matthew 24:19; Mark 13:17; Luke 21:23 (Lysias, Aristotle, others; the Sept. for הֵינִיק); μαστοίἐθήλασαν, Luke 23:29 R G.
Matthew 21:16 - V-PPA-GMP GRK:νηπίων καὶ θηλαζόντων κατηρτίσω αἶνον NAS: OF INFANTS AND NURSING BABIES YOU HAVE PREPARED KJV: and sucklings thou hast perfected INT: of little children and infants you have ordained praise
Matthew 24:19 - V-PPA-DFP GRK:καὶ ταῖς θηλαζούσαις ἐν ἐκείναις NAS: and to those who are nursing babies in those KJV: and to them that give suck in INT: and to those that nurse infants in those
Mark 13:17 - V-PPA-DFP GRK:καὶ ταῖς θηλαζούσαις ἐν ἐκείναις NAS: and to those who are nursing babies in those KJV: and to them that give suck in INT: and to those that nurse infants in those
Luke 11:27 - V-AIA-2S GRK:μαστοὶ οὓς ἐθήλασας NAS: at which You nursed. KJV: the paps which thou hast sucked. INT: [the] breasts at which you nursed
Luke 21:23 - V-PPA-DFP GRK:καὶ ταῖς θηλαζούσαις ἐν ἐκείναις NAS: and to those who are nursing babies in those KJV: and to them that give suck, in INT: and to those nursing in those