There is not currently a record recognized by Guinness World Records. Large 3x3s have been made though. The following picture is of a cube that works and is 1x1x1 meter (3 feet 3⅜ inches).
To make one and have it recognized by Guinness as a world record, there are guidelines that have to be followed. I can post a link that shows those guidelines if you want. (Are links to the TP forum okay borginator2?)