As far as I can tell, here's a history of largest computer cube solves ever:
2x2x2 - January 12, 2000, by David Barr, in 35.600
3x3x3 - January 12, 2000, by David Barr, in 1:23.600
4x4x4 - January 12, 2000, by David Barr, in 5:52.460
5x5x5 - January 12, 2000, by David Barr, in 9:20.180
6x6x6 - January 13, 2000, by David Barr, in 16:42.830
7x7x7 - January 21, 2000, by David Barr, in 23:33.450
11x11x11 - March 12, 2000, by David Barr, in 1:20:15.566
11x11x11 - June 12, 2000, by Chris Hardwick, in 56:32.298
11x11x11 - February 20, 2001, by fl, in 5:24:40.242
11x11x11 - April 11, 2001, by fl, in 6:57:35.728
11x11x11 - May 25, 2001, by fl, in 2:23:04.975
11x11x11 - May 31, 2001, by vfr, in 1:36:03.768
20x20x20 - June 12, 2001, by Chris Hardwick, in 4:24:54 (solving time) or 8:13:56 (total time)
20x20x20 - March 16, 2002, by Richard Carr, in 3:53:39.573
20x20x20 - June 25, 2002, by Richard Carr, in 3:05:27.722
20x20x20 - September 7, 2002, by Richard Carr, in 2:46:48.822
21x21x21 - October 28, 2002, by Grant Tregay, in 72:38:11.378
31x31x31 - January 1, 2003, by Richard Carr, in 7:43:15.493
35x35x35 - October 1, 2003, by Joe Allen, in 103:26:10.140
39x39x39 - October 8, 2003, by Joe Allen, in 113:48:13.052
40x40x40 - February 17, 2004, by Chris Moyer-Grice, in 23:35:xx (solving time)
55x55x55 - March 18, 2004, by Joe Allen, in 23:00:24 (solving time)
100x100x100 - December 20, 2008, by Ravi Fernando and Peter Greenwood, in 820:13:11.220
111x111x111 - May 19, 2013, by Michael Gottlieb, in 29:51:02.641 (solving time) or 246:48:xx (total time)