The Rockies' Triple-A affiliate was swept in the four-game series.
Eldred, a sixth-round pick in the 2002 Draft, has six homers and 16 RBIs in his last eight games. Sunday marked his first three-homer game as a pro and gave him 183 roundtrippers during a 10-year Minor League career. He also hit 14 in the big leagues over 74 games with Pittsburgh in 2005 and 2007.
"I'm just starting to get a good feel for things and the weather getting nicer helps out, too," said Eldred, who became the seventh Sky Sox player to go deep three times in a game. Jorge Piedra was the last to do it on July 1, 2004 at Albuquerque.
After popping up in the first inning, Eldred came up with two out in the third and the Sky Sox trailing, 2-0. He sent a solo shot over the left-field wall, then repeated the feat with two out and one on in the fifth. Both came off Cubs starter J.R. Mathes, who has allowed eight homers in nine starts.
The 6-foot-5, 290-pound Eldred flied to right in the seventh, then came up again with two out in the ninth.
"I was kind of thinking about [hitting a third homer] when I came up, but then I got two strikes and forgot about it," he said. "But I was able to get the ball up in the air and it just carried."
The 29-year-old is in his first season in the Pacific Coast League after spending parts of five seasons in the International League.
"I'd heard that the Pacific Coast League had a reputation as a hitters' league," he said. "It's been pretty exciting playing in places I haven't been before."
Sky Sox starter Josh Muecke fell to 0-3 after yielding seven runs on eight hits over 3 1/3 innings. The left-hander has surrendered 22 earned runs in 21 1/3 frames and has a .371 batting average against.
Sunday marked the 10th time this season and fifth time in the last eight games that the Sky Sox have allowed double-digit runs. Their 5.59 team ERA ranks 15th in the 16-team PCL.
Chris Nelson went 3-for-4 with a two-run homer and Jay Payton doubled and singled for Colorado Springs.
Mathes (4-4) gave up three runs on seven hits over six innings. James Adduci collected three singles and drove in four runs, while Darwin Barney went 3-for-5 with an RBI for the I-Cubs, who have won six straight games.