Answer
\[\underline{343}\]
Work Step by Step
The number of cubes can be calculated by dividing the volume of the bigger cube by the volume of the smaller cube.
\[\begin{align}
& \text{Number of smaller cubes =}\frac{\text{Volume of 7-cm cube}}{\text{Volume of 1-cm cube}} \\
& =\frac{{{\left( 7\text{ cm} \right)}^{3}}}{{{\left( \text{1 cm} \right)}^{3}}} \\
& =343
\end{align}\]
The number of 1-cm cubes in a 7-cm cube is \[\underline{343}\].
