When cavity is not present:

Electric field inside the solid sphere

$$ \overrightarrow{\mathrm{E}_{1}}=\frac{\rho}{3 \varepsilon_{0}} \overrightarrow{r_{1}} $$ ..... (i)

Solid sphere after making cavity inside solid sphere,

$$ \overrightarrow{\mathrm{E}_{2}}=\frac{\rho}{3 \varepsilon_{0}} \overrightarrow{r_{2}} $$ ...... (ii)

$${\overrightarrow E _{net}} = \overrightarrow {{E_1}} - \overrightarrow {{E_2}} = {\rho \over {3{\varepsilon _0}}}\overrightarrow {{r_1}} - {\rho \over {3{\varepsilon _0}}}\overrightarrow {{r_2}} $$

$$=\frac{\rho}{3 \varepsilon_{0}}\left(\overrightarrow{r_{1}}-\overrightarrow{r_{2}}\right) $$ ...... (iii)

From eq (iii), we get

$$\therefore \quad \mathrm{E}_{\mathrm{net}}=\frac{\rho}{3 \varepsilon_{0}}(\vec{r})$$

Hence, electric field inside the emptied space (cavity) is non-zero and uniform.