It was proved by Davenport [3] that for the nonzero integral
λ
i
{\lambda _i}
the equation
λ
1
x
1
3
+
⋯
+
λ
8
x
8
3
=
0
{\lambda _1}x_1^3 + \cdots + {\lambda _8}x_8^3 = 0
always has a nontrivial integral solution. In this paper, we investigate the bounds of nontrivial integral solutions in terms of
λ
1
,
…
,
λ
8
{\lambda _1}, \ldots ,{\lambda _8}
.