There are a couple of issues with your code
1) Indexes in MatLab start at 1, not 0, so y(0) is not valid syntax and must be replaced with y(1).
2) First index, then raise to the power, i.e. y^2(n) becomes y(n)^2
See example below (since you have not specified the value of delta, I arbitrarily replaced it with 0.1)
N = 100; % number of steps
t = linspace(0,200,N);
h = t(2)-t(1); % step size
y = zeros(1,N); % Initialization of solution (speeds up code)
y(1) = 1/100; % Initial condition
for n = 1:N-1
y(n+1) = y(n)+h*(y(n)^2-y(n)^3); % FWD Euler solved for y(n+1)
end
figure(1)
plot(t,y)
Now, the backward euler method is a bit more complicated because it's an implicit method.
You can use a root finder algorithm like fzero and do
N = 100; % number of steps
t = linspace(0,200,N);
h = t(2)-t(1); % step size
y = zeros(1,N); % Initialization of solution (speeds up code)
y(1) = 1/100; % Initial condition
for n = 1:N-1
f = @(x) x-y(n)-h*(x.^2-x.^3);
y(n+1) = fzero(f,y(n)); % BWD Euler solved for y(n+1)
end
figure(2)
plot(t,y)
