Making use of the cube root table,

We have:

$7500<7532<7600 \Rightarrow \sqrt[3]{7500}<\sqrt[3]{7532}<\sqrt[3]{7600}$

From the cube root table, we have: 

$\sqrt[3]{7500}=19.57$ and $\sqrt[3]{7600}=19.66$

For the difference $(7600-7500)$, i.e., 100 , the difference in values

$=19.66-19.57=0.09$

$\therefore$ For the difference of $(7532-7500)$, i.e., 32 , the difference in values

$=\frac{0.09}{100} \times 32=0.0288=0.029$ (up to three decimal places)

$\therefore \sqrt[3]{7532}=19.57+0.029=19.599$