Question

Find the value of 58 cube -24 cube - 34 cube

Answer 1

58×58×58=195112
24×24×24=13824
34×34×34=39304

195112-13824-39304=141984

Answer 2

For such questions, one should use algebra and avoid large number multiplications.  The calculator is not supposed to be used.

use   a³ - b³ = (a - b) (a² + ab + b²)

58³ - 24³ - 34³ 
  = (58 - 24)(58² + 58 * 24 + 24²) - 34³
  =    34 *  [ 58² +  24 (58 + 24)  - 34² ]
  =    34 *  [ 58² - 34² + 24 * 82 ]
  =    34 *  [  (58+34)(58 - 34) +  24 * 82 ]
  =    34 *  [  92 * 24 + 24 * 82 ]

  =    34 *  24 * 174
   =   17 * 12 *  4 * (175 -1)
   =   17 * 12 * (700 - 4)
   =   17  * 6 * (1400 - 8)
   =     102 * 1400 - 8 * 102
   =      142, 800 - 816

    =   141, 984