Solving with cubes, Strange!

8x8x8(single cube)=512 $cm^{3}$

let total number of $2*2*2$ cubes be ''a''

then :- $8a+512$ = $1728$

8a=1216

a= $\boxed{152 }$

Equivalently, we can calculate the number of $1\times 1\times 1$ cubes we need to add to a $4\times 4\times 4$ cube to form a $6\times 6\times 6$ cube, which is equal to $6^3-4^3=216-64=\boxed{152}$ .

2x2x2 will have 8 cubes,

8x8x8 will have 512 cubes,

12x12x12 will have 1728 cubes,

so (1728-512)/8=152

8 8 8 = 512

12 12 12 = 1728

1728 - 512 = 1216

2 2 2 = 8

1216 / 8 = 152

Let $m$ be the number of $2 \times 2 \times 2$ cubes needed, then

$m=\dfrac{12^3 - 8^3}{2^3}=\boxed{152}$

volume of cube measuring 8 units

v8 = 8³ = 512 cubic units

volume of cube measuring 12 units

v12 = 12³ = 1728 cubic units

difference in volume

v12 - v8 = 1728 - 512 = 1216 cubic units

volume of cube measuring 2 units

v2 = 2³ = 8 cubic units

divide the difference in volume by the volume of cube measuring 2 units

1216/8 = 152 cubes

How to do this if you're lazy and don't have a calculator:

$\frac{12^3 \times 8^3}{2^3}$
$= 6^3 - 8^2 = 2^3 (3^3 - 2^3)$
$= 8 \times 19 = 8 \times 20 - 8$
$= 160-8 = \fbox{152}.$

To form 12x12x12 =1728 minus 8x8x8 =512 divide by 2x2x2=8

n= (12^3)-(8^3)=1216/8 = 152 :)

12x12x12=1728

8x8x8=512

2x2x2=8

1728-512=1216

1216/8=152

2^3=8 8^3=512 12^3=1728 2^3 x + 8^3 = 12^3 8x + 512 = 1728 8x = 1728-512 8x=1216 x=152

(12 12 12)-(8 8 8) = 1216/(2 2 2) = 152

simply 2³x + 8³ = 12³

or x = (12³ - 8³)/2³

x = 152