Math equation, 8th grade fractions

A 2x2x2 cube is removed from each corner of an 8x8x8 cube. What fraction of the original cube remains? express your answer as a common fraction.

Please and thank you!
And if you could please show me how you got the answer I'll really appreciate it thanks again!:)

Remaining Vol= 8^3 - 4(2^3) = 512 - 8(8) = 512 - 64 =448
Fraction remaining = 448 / 512 = 87.5% or 7/8
Answer

A 2 x 2 x 2 cube is removed from each corner of an 8 x 8 x 8 cube.
What fraction of the original cube remains?
Number of corners in a cube is 8.
Volume of cubes removed is 8 x 8 cubes
Fraction of original cube remaining 8 cube
express your answer as a common fraction.

The original volume was 8 * 8 * 8 = 512
The volume removed was 8 * (2 * 2 * 2) = 64
The remaining volume is 512 - 64 = 448

448/512 = 7/8

There are 8 corners to a cube so if you are taking away 8 2x2x2 cubes from the 8 cube the fraction based on the volume will be:

[8x8x8 - 8(2x2x2)]/(8x8x8) = 0.875 = 7/8

(8x8x8-2x2x2)/(8x8x8)=(512-8)/512=504/51…