**Step 1. Calculate the number of sugar cubes**

#"No. of sugar cubes" = 2.7 color(red)(cancel(color(black)("mol cubes"))) × (6.02 × 10^23color(white)(l) "cubes")/(1 color(red)(cancel(color(black)("mol cubes")))) = 1.63 × 10^24 color(white)(l)"cubes"#

**Step 2. Calculate the volume of the cubes**

**(a)** Calculate the volume of one cube

#V = l^3 = ("1.0 cm")^3 = "1.0 cm"^3#

**(b)** Calculate the volume of all the cubes

#V = 1.63 × 10^24 color(red)(cancel(color(black)("cubes"))) × "1.0 cm"^3/(1 color(red)(cancel(color(black)("cube")))) = 1.63 × 10^24 color(white)(l)"cm"^3#

**Step 3. Calculate the edge length of the large cube**

#l = root(3)(1.63 × 10^24 color(white)(l)"cm"^3) = 1.2 × 10^8color(white)(l) "cm" = 1.2 × 10^6 color(white)(l)"m" = 1.2 × 10^3color(white)(l) "km"#