What is the value of the given periodic signal at any time, how to solve it in MATLAB?
Assuming continuous-time for the probem, for all periodic signals with a period of $T$ , for any integer $m$ , we have :
$$  x( t + mT) = x(t) \tag{1}$$
So, for example with  $T=7$ , and $m=2$ , you can see that $x(15) = x(2\cdot 7 + 1) = x(1)$. The operator that is used to find base argument for a given $t$ value is the modulus :
$$ x(t) = x( \text{mod}(t,T) ) \tag{2}$$
where $\text{mod}(t,T)$ is the modulus of $t$ wrt $T$.
For your example, your period is $T=7$, and you can see that $x(315) = x( \text{mod}(315,7) ) = x(2)$.
Hence the value of $x(t)$ for $t=2$ is $0.1 \cdot 2^3 = 0.8$.
I don't know if there's anything to solve with MATLAB here though?