A cube has 6 identical square faces.

1. THE FRONT FACE
2. THE BACK FACE
3, THE RIGHT FACE
4. THE LEFT FACE
5. THE TOP FACE
6. THE BOTTOM FACE

Each face is a square (1 foot 9 inches) by (1 foot 9 inches)

9 inches is  of a foot or  of a foot or 0.75 feet

So each of the 6 square faces has area = (6.75)² or 45.5625 square feet. 

Therefore the entire surface area if 6×45.5625 sq. ft. or 273.375 sq. ft.

If you'd rather have it as a fraction and not a decimal, .375 = 

So the answer is 273.375 sq. ft. or  sq. ft.

[Note: Area must be in square feet, not feet]

Edwin