The edge of a cube is measured 2% too long. By what percent will the volume calculated from that measurement be too large?

The volume goes as the cube of the edge, so it is out by a factor of $1.02^3=1.061208$ — an excess of 6.1208%, which rounds to 6.12%. (6% takes $3\times 2$% and drops the small cross-terms, a fair estimate but not the exact figure asked for; 2% forgets that the error is cubed; 8% comes from $4\times 2$%, the factor for no dimension at all.)