Explanation:

Using algebraic identities,
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
By putting the respective values given in question,
⇒ (9)² = a² + b² + c² + 2(ab + bc + ca) [? ab + bc + ca = 26]
⇒ (9)² = a² + b² + c² + 2(26)
⇒ a² + b² + c² = 81 - 52 = 29
Given equations,
a³ + b³ = 91      ----(1)
b³ + c³ = 72      ----(2)
c3 + a3 = 35      ----(3)
On adding (1), (2) and (3)
a³ + b³ + b³ +c² + c² + a³ = 91 + 72 + 35
⇒ 2(a³ + b³ + c³) = 198
⇒ a³ + b³ + c³ = 99
Using algebraic identities,
a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - ab - bc - ca)
By putting the respective values,
⇒ 99 - 3abc = 9 (29 - 26) [? ab + bc + ca = 26 and a + b + c = 9]
⇒ 3abc = 99 - 27
⇒ abc = 72/3
∴ abc = 24